Face Identification Using Thermal Images with

CORF detector and measuring the Similarity Index

using FSIM and SSIMSudheer Reddy Bandi

1 D Sheela

2 Merlin Linda

3

1Assistant Professor Department of Computer Science and Engineering Tagore Engineering College Chennai-600127

2Professor Department of Electronics and Communicat ion Engineering Tagore Engineering College Chennai-600127

3Research Scholar Tagore Engineering College Chennai-600127

1bsudheer115gmailcom

2dsheelatagoreranddgmailcom

3merlinlindagmailcom

Abstractmdash Human Computer Interaction or the identification

of humans by machines plays a key role in the social

environment To have a better authentication or identification

rate biometrics plays a dynamic role in the present day scenario Due to the special properties of thermal images like itsnon-

contact and non-intrusive mechanism face detection using

infrared images gained interest in various current

applicationsThe objective of the present work is distributed into

three stages as segmentation Combination of Receptive Fields (CORF) edge detection and Image Quality Assessment (IQA)

The Darwinian Particle Swarm Optimization (DPSO) technique

performs the segmentation of the thermal face images in turn

carried by the Chan-Vese active contour image segmentation to

produce the binary form of face image database from the standard database of DPSO segmented images The second stage

extracts the contour of image using CORF operator which

operates on the visual cortex of simple cells using Difference of

Gaussian (DoG) and Gabor filters In the final stage the CORF

edge detected images are compared based on the similarity index of IQA techniques like FSIM (Feature Similarity Index

Measurement) and SSIM (Structure Similarity Index

Measurement) In this new area of exploration the subjective

and objective results of the experiments conducted indicates that

the addition of stochastic based DPSO image segmentation along with the Chan-Vese active contour image segmentation gives

better results to identify the thermal face images and the FSIM

and SSIMare better quality image assessments to compare the

similarity of infrared face images

KeywordsmdashIdentification Image Quality Assessment Infrared

Swarm Intelligence Active Contour Similarity Index

I INTRODUCTION

Bio stands for bdquobiology‟ and metric stands for bdquomeasurement‟ The accurate measurement of various

biological or physiological b iometrics are used to identify or

detect an individual Various biological identit ies are fingerprint Palmprint iris hand geometry face and DNA

whereas behavioral characteristics are keystroke voice recognition and signature verificationThe foremost

applications of biometrics is in the field of security hospital management banks educational institutions multinational

companies and so on Facial (face) recognition which is one

of the physical biometric identification traits has become an interesting research topic in the present world of pattern

recognition and machine vision [1] Face recognition is widely

recognized due to the feasibility and the unobtrusive nature of

capturing facial images Significant and enough work has been obtained in face recognition in the visible spectrum [2] The

face of a person have a numerous distinguishable

characteristics like distance between eyes width of the nose depth of the eye sockets the shape of the cheekbones and the

length of the jaw line Visible facial images face difficu lties in the form of illumination and occlusion There are few other

trustworthy techniques like iris finger and palmprint authentication techniques which face a problem like difficu lty

in gathering the features of the individual‟s biometrics To overcome the aforementioned disadvantages one solution is to

go for infrared face image recognition [3]

The various advantages of Thermal IR spectrum for the

face recognition are it can visualize the facial images without

illumination ie even in darkness robust to facial recognition

In addition to the aforementioned thermal IR sensors are less

affected by scattering and the absorption by smoke

anatomical structure can be clearly understood by the Infrared

sensors and especially thermal sensors measure the emitted

heat energy but do not measure the reflected energy from

thermal facial images Any technique is limited to certain

threshold in which the limitations of IR technique aresubject

to environmental temperature emotional physical and health

conditions Drinking alcohol can also affect the thermal image

of the face Another problem of the thermal spectrum is the

opaqueness to eyeglasses This makes a large portion of the

face wearing eyeglasses to be occluded in thermal images So

some information around the eyes will be lost [4]

II RELATED WORK

Large corpus of work have been done in the area of

Infrared based face recognition The state of the art techniques

regarding thermal image face recognition is mainly classified

into the following categories i) Holistic based approaches ii)

Feature based approaches iii) Fusion based techniques and

multispectral based methodsRegarding appearance based

techniques one of the earlier works by Prokoski et al [5] in

which the elementary shapes are extracted from thermograms

which appears like fingerprints Effectiveness and accuracy of

the published work is not recordedCutler et al [6] used the

automatic infrared face recognition in which his method was

based on eigenfaces in which he achieved recognition

International Journal of Pure and Applied MathematicsVolume 118 No 20 2018 135-145ISSN 1314-3395 (on-line version)url httpwwwijpameuSpecial Issue ijpameu

135

accuracy of 96 for frontal and semi-profile views and 100

accuracy rate for profile v iews and compared the results with

the visible images and achieved the promising results

Socolinsky et al [7] [8] used linear methods like Principal

Component Analysis (PCA) Linear Discriminant Analysis

(LDA) and Independent Component Analysis (ICA) and the

results reinforced the research methodologies in thermal facial

images and results were compared with visible face images

But in all the above mentioned survey some limitations were

applied like challenges in the data set less time lapse was

maintained no thermal image with glasses and pose or

expression were consideredIn the works of Tzeng et al [9]

Arandjelovic et al [10] Jin et al [11] Bourlai et al [12] and

Martinez et al [13] focussed on eyes localizat ion errors and

registration errors were reported

In Chen et al [14] work there was a considerable

reduction in the recognition rates of thermal facial images

when small localization errors were synthetically introduced to

manually marked eye positions Zhao et al [15] used active

Near Infrared data and solved the problem of localizing the

eyes in passively acquired images In this paperNIR lighting

source was placed and aligned with the camera axis is used to

illuminate the face Because the interior of the eyes reacts the

incident light the pupils appear distinctively bright and as such

are readily detected in the observed image (the so-called bright

pupil effect) Zhao et al used the locations of pupils to

register images of faces which are then represented using

their DCT coefficients and classified using a support vector

machineIn recent advances in appearance based methods

Elguebaly and Bouguila [16] described a method based on a

generalized Gaussian mixture model theparameters of which

are learnt from a training image set using a Bayesian approach

and achieved approximately 95 rank-1 rate

Feature based method is the second approach in the

infrared based face image segmentation An early method of

feature extraction method was proposed by Yoshitomi et al

[17] In this paper the approach of neural network with gray

level h istograms was combined and achieved a recognition

rate of 92 But the increase in temperature difference

between training and testing data decreased the rate of

detection Li et al [18] have done a lot of research in thermal

face image detectionusing local binary patterns The research

was done in closed environment and room temperatures and

the work resulted in good results But the drawback was that

the technique was unsuitable for outdoor environmental

conditions Maeng et al [19] also applied local binary patterns

in which the results were not efficient whereas SIFT (Scale-

Invariant Feature Transform) based features providing

impressive results Goswami et al [20] worked on variations of

local binary patterns and compared the results Wavelet

transform using Gabor filters were first implemented by

Srivastava et al [21] The results outperformed the holistic

based approaches of independent component analysis and

eigenfaces The curvelet transform is an extension of wavelet

transform which was first implemented by Xie et al [22] in the

infrared facial images and achieved increase in recognition

rate of 1-2 over other conventional wavelet transform

techniques Buddharaju et al [23][24] published first work on

vascular features followed by the contributions of Gault et al

[25]and Seal et al [26] The work of these authors extracted

blood vessels from thermal images using simple

morphological filters Cho et al [27] modified the approach of

Buddharaju et al on Equinox database and the results were

better and overtook Adaboost class ifiers mult ilayer

perceptron and Naiumlve Bayes classification The contribution

by Ghiass et al [28] were better than previous works on

vascular networks by applying Active Appearance Models on

pose variations and gave the proof of extracting the actual

blood vessels from vascular structures Wu et al [29] and Xie

et al [30] worked on blood perfusion model Wu et al took

the original segmented thermograms and the output images

were b lood perfusion image data were matched using RBF and

linear discriminant analysis where as Xie et al proposed a

model based on pennes equation whose results were better

than Wu et al

In our work a unique approach has been followed by the

segmentation fusion of PSO based image segmentation and

Active contour without edges In the second stage post

processing is done by CORF detector and the results are

matched with FSIM and SSIM

III PROPOSED WORK

The methodology of the proposed work is represented in

Figure 1

A DPSO based Image segmentation

Particle Swarm Optimization (PSO) is a random distribution

based search technique of Swarm Intelligence which involves

the movement of entities like school of birds or flock of fish

given by Kennedy and Eberhart [31] in 1995 PSO is also an

optimization technique or stochastic technique to find the best

solution among the given candidate solutions A simple

formulae is applied on particle‟s position and velocity There

are three variants of PSO in image segmentation which

includes (i) Darwinian Particle Swarm Optimizat ion ([32]

[33]) (ii) Fract ional-Order Darwinian Part icle Swarm

Optimization ([34] [35]) and (iii) Binary Fract ional Order

Darwin ian Part icle Swarm Opt imization [36]

International Journal of Pure and Applied Mathematics Special Issue

136

Fig 1 The proposed Sudheer-Sheela automatic thermal face detection framework using DPSO and Active Contour image segmentation

Enrichments were given to the original PSO by Tillett et al

[32] and developed a type of PSO technique called as

Darwin ian PSO which is implemented in this paper DPSO is

one of the variant of PSO in which number of swarms of test

solutions may exist at any time The performance of the each

individual swarm looks similar to an ordinary PSO algorithm

with some guidelines and rules that are designed and planned

to simulate natural selection This type of natural selection is

termed as Darwin ian principle of Survival of the fittest Each

swarm individually performs optimization just like a PSO

algorithm with some rules governing the collection of thermal

face image

The image segmentation procedure described in [37] is given here Let there be L intensity levels in each component

three color components for RGB images of a given image and these level are in the range 012hellip 119871 minus 1

119901119894119862 =

119893119894119862

119873 119901119894

119862 = 1119871 minus 1

119894 = 0 (1)

wherei represents a specific intensity level ie 0 le 119894 le 119871 minus1 C represents the component of the image 119862 = 119877119866 119861 for

RGB imagesN represents the total number of pixels in the image and 119893119894

119862 denotes the number of pixels for the

corresponding intensity levels i in component C or 119893119894119862

represents an image histogram for each component C which can be normalized and regarded as the probability

distribution119901119894119862 The total mean of each component of the

image can be easily calculated as

120583119879119862 = 119894119901119894

119862 = 1119871 minus 1

119894 = 0 (2)

The probabilit ies of occurrence 119908119895119862 of classes 1198631

119862hellip 119863119899119862

are given by

119908119895119862 =

119901119894

119862 119905119895119862

119894 = 0 119895 = 1

119901119894119862

119905119895119862

119894 = 119905119895 minus 1119862 + 1

1 lt 119895 lt 119899

119901119894119862

119871 minus 1

119894 = 119905119895 minus 1119862 + 1

119895 = 119899

(3)

The mean of each class 120583119895119862 can then be calculated as

120583119895119862 =

119901119894119862

119908119895119862 119902

119905119895119862

119894 = 0 119895 = 1

119901119894119862

119908119895119862

119905119895119862

119894 = 119905119895 minus 1119862 + 1

1 lt 119895 lt 119899

119901119894119862

119908119895119862 119871 minus 1

119894 = 119905119895 minus 1119862 + 1

119895 = 119899

(4)

The simplest and computationally most efficient method of obtaining the optimal threshold is the one that maximizes the

between-class variance of each component which can be generally defined by

1205901198611198622

= 119908119895119862 120583119895

119862 minus 120583119879119862

2119899119895 = 1 (5)

wherei represents a specific class in such a way that 119908119895119862 and

120583119895119862 are the probability of occurrence and the mean of class j

respectivelyThe problem of n-level thresholding is reduced to

an optimization problem to search for the thresholds 119905119895119862 that

International Journal of Pure and Applied Mathematics Special Issue

137

maximize the objective functions (ie fitness function) of

each image component C generally given in equation 6 and the model results are displayed in Figure 2

120593119862 = max

1lt1199051119862 lt⋯lt119871minus1

1205901198611198622

119905119895119862 (6)

Fig 2 (a) Thermal images and (b) DPSO segmented images

B Active Contour Image Segmentation

Image segmentation is a central task in solving the region of

interest problem in image processing In general there are

three conventional methods of image segmentation procedures

like pixel based methods region based methods and edge

based methods all of which depends the local information of

the image [38] In our paper hybrid approach to image

segmentation is introduced named as Active contours without

edges [39][40] helps to find object boundary in a given image

based on curve evolution technique [41][42] popularly known

as level set method The basic impression of the level set

method or any active contour method is to evolve a curve over

time so that the curve moves towards its interiornormal and

when the stopping conditions are met the curve forms an

outline around theobject of interest For a g iven image 119868 [43]

we can create a level set function empty 119909 119910 withthe same size o f

the image 119868to describe the contour The contour is defined as

the zerolevel set of the function emptyas given in equation 7

119862 = 119909 119910 119891 119909 119910 = 0 (7)

(i) Energy Equation

The evolution of the initial contour is guided by an energy equation For the contour with an Signed Distance Function

(SDF) (empty119888 119909 119910 ) the energy function can be expressed as

119864 119862 = 119864 empty119888 119909 119910 = 1199081119864119868119898119886119892119890 119862 + 1199082119864119878119893119886119901119890 119862 +

1199083119864119877119890119892119906119897119886119903119894119911119886119905119894119900119899 119862 (8)

Where1199081 1199082and 1199083are real valued positive constant

weighting factors The image term119864119868119898119886119892119890 119862 attracts the

contour towards the object boundary 119864119878119893119886119901119890 119862 the shape

term penalizes the curve for deviating from uniformlayer

thickness [44] Lastly the regularizat ion

term119864119877119890119892119906119897119886119903119894119911119886119905119894119900119899 119862 helps to create a min imal length

smooth contour [45]Based on the combination of these energy

equation components (empty119888 119909 119910 ) is deformed to min imize

(empty119888 119909 119910 119905 )

(ii) Image term

119864119868119898119886119892119890 119862 =

1205821 119868 119909 119910 minus 1198881 2119889119909119889119910

119903119890119892119894119900119899 119887119890119905119908119890119890119899 119862119894 119886119899119889 119862119894minus1

+ 1205822 119868 119909 119910 minus 1198882 2

119903119890119892119894119900119899 119887119890119905119908119890119890119899 119862119894 119886119899119889 119862119894+1119889119909119889119910(9)

The image term divides the image into regions inside and

outside of the contour 119862 The values 1198621and 1198622are the values

of the mean pixel intensity inside and outside of the contour

respectively The constants 1205821and1205822are constants typically

both set to 1 This term reaches a minimum when the contour

divides the area inside and outside in regions of constant

homogeneity ie when lies along an object boundary [46]

Using the level set formulation the image term can be

expressed as

119864119868119898119886119892119890 = 1205821 119868 119909 119910 minus 1198881 2119867 empty119894 minus 1 119909 119910 1

minus 119867 empty119894 119909119910 119889119909119889119910

+ 1205822 119868 119909 119910 minus 1198882 2119867 empty119894 119909119910 1 minus 119867 empty119894+ 1 119909119910 119889119909119889119910

(10)

Where

119867 empty119894 minus 1 119909119910 1minus 119867 empty119894 119909119910 119886119899119889 119867 empty119894 119909 119910 1 minus

119867 empty119894+ 1 119909119910 are used to select the regions inside and

outside respectively

(iii) Shape term

The shape term is to say that each layer should be parallel to

the layer immediately above it Thus the shape term was

designed to penalize movement away from consistent

distances between boundaries For the boundary the boundary

is used for comparison The shape term is expressed by

119864119878119893119886119901119890 119862119894

= 119898119886119909 0 119862119894 119909 minus119862119894 minus 1 119909 minus 119880119894 119862119894 119909 minus 119862119894 minus 1 119909 minus119909119871119894 119889119909 (11)

Using the level set formulation the shape force term becomes

119864119868119898119886119892119890 empty119894 119909119910 = 119898119886119909 0 119910 minus119862119894 minus 1 119909 minus119880119894 119910 minus

119862119894 minus 1 119909 minus 119871119894 120575 empty119894 119909 119910 |nablaempty119894 119909 119910 |119889119909119889119910

(12)

Where120575 empty119894 119909 119910 |nablaempty119894 119909 119910 |is used to select the current

boundary region

(iv) Regularization term

International Journal of Pure and Applied Mathematics Special Issue

138

The last term in the regularizat ion is used to encourage

smooth short contours [47] The force term can be expressed

simply as

119864119877119890119892119906119897119886119903119894119911119886119905119894119900119899 empty119894 119909119910 = 120575 empty119894 119909119910 |nablaempty119894 119909119910 |119889119909119889119910 (13)

The results of the active contour image segmentation are

displayed in Figure 3 and histogram representations are given

in Figure 4

Fig 3 Top row DPSO segmented images Bottom row Active contour

segmented images

Fig 4 (a) Thermal image(b) Histogram representation of thermal image (c) DPSO segmented image (d) DPSO segmented histogram representation (e) Active contour segmented image (f) Histogram of Active contour image

C CORF edge detector

The implementation of the proposed CORF operator is rather

straightforward it includes blurring (achieved by convolving

with a Gaussian function) of halfwave rectified responses of

DoG operators shifting appropriately these blurred res ponses

by different vectors which are determined in the configuration

of the operator and using them for the pixel-wise evaluation

of a weighted geometric mean that gives the output of the

CORF operatorWe apply a classical two-step procedure in

computer vision thatwas proposed by [48] and [49] to obtain a

binary contour mapfrom the output of the concerned model

The first step consists ofedge thinning by non-maximum

suppression to determine theridges in the given response

image Then we apply hysteresis thresholding to obtain a

binary contour map The latter steprequires a high and a low

threshold value Similar to the work in[50] we set the low

threshold value to a fraction (05) of the highthreshold For a

given image we set the high threshold to be thelowest value

of the strongest f pixels in the thinned responseimage The

given value of the parameter f is a fraction of the totalnumber

of pixels in the image The resulting binary map containsthe

strongest fraction f of contour pixels together with

anyconnected ones that are achieved by hysteresis

thresholding The parameters used for the CORF operator are

the number of orientations nϴ (n=12 for ϴ=П6) a scale

parameter σ wavelength λ= σ4 and a spatial aspect ratio

γ=05

(i) Non-maximum suppression edge thinning

TheNon-maxima suppression thins the areas in which

119862120590 119909 119910 is non-zero to one-pixel wide candidate contours as

follows For each position 119909 119910 two responses Cσ(x|y

|) and

Cσ(x||y

||) in adjacent positions (x

|y

|) and (x

||y

||) that are

intersection points of a line passing through 119909 119910 in

orientation 120579120590 119909 119910 and a square defined by the diagonal

points of an 8-neighbourhood are computed by linear

interpolation as given by Figure 5 If the response

119862120590 119909 119910 at 119909 119910 is greater than both these values (ie it is a

local maximumalong the concerned line) it is retained

otherwise it isassigned the value zero

Fig 5 Interpolated responses at positions (x|y

|) and (x

||y

||) Non-

maximasuppression retains the value in the central pixel ethx yTHORN if it is larger

than thevalues at (x|y

|) and (x

||y

||)

Fig 6 (a) Image after active contour segmentation (b) One pixel binarized hysteresis threshold image (c) Image after CORF edge detection

International Journal of Pure and Applied Mathematics Special Issue

139

ii) Binarizat ion by Hysteresis thresholding

Next a binary map is computed from the candidate contour

pixels by hysteresis thresholding This process involves two

threshold values TLand TH TLltTH Commonly the high

threshold value THis computed as a (1-p)-quantile of the

distribution of the response values at the candidate contour

pixels where p is the minimum fraction of candidate pixels to

be retained in the contour map Candidate contour pixels with

responses higher than th are definitely retained in the contour

map while the ones with responses below the low threshold

TLare discarded Candidate contour pixels with responses

between TLand THare retained if they can be connected to any

candidate contour pixel with a response higher than THthrough

a chain of other candidate contour pixels with responses larger

than TL Figure 6 gives the results of edge thinning by non-

maximum suppression to one pixel and CORF edge detection

by hysteresis thresholding

D FSIM and SSIM

The aim of objective Image Quality Assessment (IQA) is to

develop mathemat ical models that are able to forecast the

quality of an image precisely and spontaneously An ideal

objective IQA method should be able to simulate the quality

predictions of an average human observer The proper IQA

method calculates the similarity index using a mathemat ical

model by quantizing the distortion image and the reference

image The main feature of the proper IQA is that it can be

embedded in real t ime image processing system The most

advanced method to perform IQA is Structure Similarity Index

Measurement (SSIM) [51] The various features like

luminance contrast and structure are compared in the SSIM

Almost all these features are consistent with the Human

Visual System (HVS) and are compatible But there are few

drawbacks as the luminance and contrast are sensitive to the

illumination To overcome the drawbacks of the

aforementioned technique Feature Similarity Index

Measurement (FSIM) has come into existence [52] In FSIM

two features main ly Phase Congruency (PC) [53] [54] and

Gradient Magnitude (GM) are considered To compute the PC

of 2D grayscale images The 1D log-Gabor filters described

earlier can be extended to 2D ones by simply applying some

spreading function across thefilter perpendicular to its

orientation One widely used spreading functionis Gaussian

[55] [56] and [57] By using Gaussian as the spreading

function the 2D log-Gabor function has the following transfer

function

1198662 120596120579119895 = 119890119909119901 119897119900119892 120596 1205960

2

21205901199032

119890119909119901 120579minus120579119895

2

21205901205792

(14)

Where 120579119895 = 119895120587 119869 119895 = 01hellip 119869 minus 1 the orientation angle of

the filter is 119869 is the number of orientations and 120590120579determines

the filter‟s angular bandwidthBy modulat ing 120596120579 and 120579119895 and

convolving 1198662with the 2D image we get a set of responses at

each point x as 119890119899120579119895 119883 119874119899 120579119895

119883 The local amplitude on

scale n and orientation 120579119895is119860119899120579119895 119883 = 119890119899 120579119895

119883 2 +119874119899 120579119895 119883 2

and the local energy along orientation 120579119895 is119864120579119895 119883 =

119865120579119895 119883 2 + 119867120579119895

119883 2 where119865120579119895 119883 = 119890119899 120579119895

119883 119899 and

119867120579119895 119883 = 119900119899 120579119895

119883 119899 The 2D PC at x is defined as

1198751198622119863 119883 = 119864120579 119895

119883 119895

휀+ 119860119899 120579 119895 119883 119895119899

(15)

It should be noted that 1198751198622119863 119883 is a real number within 0~1

(i) The FS IM index

The computation of FSIM index consists of two stages In the

first stage the local similarity map is computed and then in

the second stage we pool the similarity map into a single

similarity score We separate the feature similarity

measurement between 1198911 119883 and 1198912 119883 into two

components each for PC or GM First the similarity measure

for 1198751198621 119883 and 1198751198622 119883 is defined as

119878119875119862 119883 =21198751198621 119883 1198751198622 119883 +1198791

11987511986212 119883 +1198751198622

2 119883 +1198791 (16)

where 1198791 is a positive constant to increase the stability of SPC

(such a consideration was also included in SSIM [51]) In practice the determination of 1198791 depends on the dynamic

range of PC values Equation 16 is a commonly used measure

to define the similarity of two positive real numbers and its

result ranges within [0 1] Similarly the GM values 1198661 119883

and 1198662 119883 are compared and the similarity measure is defined

as

119878119866 119883 =21198661 119883 1198662 119883 +1198792

11986612 119883 +1198662

2 119883 +1198792 (17)

where 1198792 is a positive constant depending on the dynamic

range of GM values In our experiments both 1198791 and 1198792 will

be fixed to all databases so that the proposed FSIM can be conveniently used Then 119878119875119862 119883 and 119878119866 119883 are combined to

get the similarity 119878119871 119883 of 1198911 119883 and 1198912 119883 We define

119878119871 119883 as

119878119871 119883 = 119878119875119862 119883 120572

119878119866 119883 120573

(18)

where 120572 and 120573 are parameters used to adjust the relative

importance of PC and GM features In this paper we set 120572 = 120573 =1 for simplicity Thus119878119871 119883 = 119878119875119862 119883 119878119866 119883 Having

obtained the similarity 119878119871 119883 at each location 119883 the overall

similarity between 1198911and 1198912 can becalculated However

different locations have different contributions to HVS‟

perception of the image For example edge locations convey

more crucial v isual information than the locations within a

smooth area Since human visual cortex is sensitive to phase

congruent structures [54] the PC value at a location canreflect

how likely it is a perceptibly significant structure point Intuitively for a given location 119883 if anyone of 1198911 119883 and

1198912 119883 has a significant PC value it implies that this position x

International Journal of Pure and Applied Mathematics Special Issue

140

will have a high impact on HVS in evaluating the similarity between 1198911 and 1198912 Therefore we use 119875119862119898 119883 =

max(1198751198621 119883 1198751198622 119883 ) to weight the importance of 119878119871 119883 in

the overall similarity between 1198911 and 1198912 and accordingly the

FSIM index between 1198911and 1198912 is defined as

119865119878119868119872 = 119878119871 119883 119883 isinΩ 119875119862119898 119883

119875119862119898 119883 119883isinΩ (19)

where Ω means the whole image spatial domain

(ii) Structural similarity index (SSIM)

The SSIM algorithm performs similarity measurement in three

steps luminance comparison contrast comparison and

structure comparison First the luminance of each image

signal is compared The estimated mean intensity is computed

as follows

120583119903119890119891 =1

119882119867 119868119903119890119891 119894 119895

119882119894 = 1

119867119895 = 1 (20)

The luminance comparison function 119897 119868119903119890119891 119868119905119904119905 is a

function of 120583119903119890119891 and 120583119905119904119905Second the contrast of each image

signal is compared For estimat ing the contrast standard

deviation is being used An unbiased estimate of standard

deviation in discrete form is as follows 120590119903119890119891

= 1

119882119867minus1 119868119903119890119891 119894 119895 minus 120583119903119890119891

2119882119894 = 1

119867119895 = 1

1

2

(21)

The contrast comparison function 119888 119868119903119890119891 119868119905119904119905 is a function

of120590119903119890119891 and 120590119905119904119905 Third the structure of each image signal is

compared Structure comparison function119904 119868119903119890119891 119868119905119904119905 is a

function of 119868119903119890119891 minus 120583119903119890119891 120590119903119890119891 and

119868119905119904119905 minus 120583119905119904119905 120590119905119904119905 Finally three comparison functions are

combined and an overall similarity measure is produced The

overall similarity measure119878 119868119903119890119891 119868119905119904119905 is a function of

119897 119868119903119890119891 119868119905119904119905 119888 119868119903119890119891 119868119905119904119905 119888 119868119903119890119891 119868119905119904119905 and 119904 119868119903119890119891 119868119905119904119905

Definitions of119897 119868119903119890119891 119868119905119904119905 119888 119868119903119890119891 119868119905119904119905 and119904 119868119903119890119891 119868119905119904119905 are as

follows

For luminance comparison function we have

119904 119868119903119890119891 119868119905119904119905 =2120583119903119890119891 120583119905119904119905 +1198791

1205831199031198901198912 +120583119905119904119905

2 +1198791 (21)

where 1198791 is a positive stabilizing constant chosen to prevent

the denominator from becoming too small We have

1198791 = 1199051119863 2 (22)

where D is the dynamic range of pixel values and 1199051 ltlt 1 is

a small constant For contrast comparison function we have

119888 119868119903119890119891 119868119905119904119905 =2120590119903119890119891 120590119905119904119905 +1198792

1205901199031198901198912 +120590119905119904119905

2 +1198792 (23)

where 1198792 = 1199052119863 2is a positive stabilizing constant

And1199052 ltlt 1 For structure comparison function we have

119904 119868119903119890119891 119868119905119904119905 =120590119903119890119891 119905119904119905+1198793

120590119903119890119891 120590119905119904119905 +1198793 (24)

where 1198793 is a positive stabilizing constant In (58)120590119903119890119891 119905119904119905 is

the correlation coefficient between the reference and test images In the discrete form120590119903119890119891 119905119904119905 can be estimated by

120590119903119890119891 119905119904119905 =1

119882119867minus1 119868119903119890119891 119894 119895 minus 120583119903119890119891 119868119905119904119905 119894 119895 minus

119882119894 = 1

119867119895 = 1

120583119905119904119905 (25)

Finally structural similarity index is defined as

119878119878119868119872 119868119903119890119891 119868119905119904119905 =

119897 119868119903119890119891 119868119905119904119905 120572 119888 119868119903119890119891 119868119905119904119905

120573 119904 119868119903119890119891 119868119905119904119905

120574 (26)

where 120572 120573 and 120574The universal quality index (UQI) [5960] is a special case of the SSIM index when1198791 = 1198792 = 1198793 = 0

and 120572 = 120573 = 120574 = 1 Since image statistical features and

distortions are usually space-variant authors of [60] employ

the SSIM index locally instead of globally Another reason for

this is that by applying the SSIM index locally a quality map

of the image which conveys more information about the

quality degradation can be generated

TABLE I SAMPLE TEN SUBJECT‟S FSIM VALUES WITH RESPECT TO EACH OTHER

Subject No

11 12 13 14 15 16 17 18 19 20

11 9342 7906 7438 7442 7648 7566 7509 78 7441 7597

12 7906 9523 734 7135 7459 745 7394 7505 7335 7449

13 7438 734 9705 743 7943 7264 776 7417 7941 7735

14 7442 7135 743 9429 8081 7252 7428 7478 7604 7406

15 7648 7459 7943 8081 943 7734 818 7903 834 8126

16 7566 745 7264 7252 7734 9247 7599 8769 7523 7713

17 7509 7394 776 7428 8189 7599 934 7552 8102 8612

18 7801 7505 7417 7478 7903 8769 7552 9342 7631 7669

19 7441 7335 7941 7604 834 7523 8102 7631 9693 806

20 7597 7449 7735 7464 8126 7713 8612 7669 806 9479

International Journal of Pure and Applied Mathematics Special Issue

141

TABLE II SAMPLE TEN SUBJECT‟S SSIM VALUES WITH RESPECT TO EACH OTHER

Subject No

11 12 13 14 15 16 17 18 19 20

11 9044 7333 6507 6937 7054 7217 6717 7433 6588 6854

12 7333 9327 6249 6298 6574 6905 6357 6976 6258 6421

13 6507 6249 9643 6744 7311 6586 7173 671 7242 7014

14 6937 6298 6744 9155 7673 6857 6911 7007 7009 6874

15 7054 6574 7311 7673 9158 7325 7676 7475 7685 7621

16 7217 6905 6586 6857 7325 925 711 867 694 7189

17 6717 6357 7173 6911 7676 711 9147 7083 7443 822

18 7433 6976 671 7007 7475 867 7083 9236 7054 7145

19 6588 6258 7242 7009 7685 694 7443 7054 9495 7423

20 6854 6421 7014 6874 7621 7189 822 7145 7423 9251

IV EXPERIMENTAL RESULTS AND ANALYSIS

In this section the performance of IQA techniques like FSIM

and SSIM are evaluated The parameters required in the

proposed methods were set as n = 4 J = 4 σr = 05978 σθ =

06545 T1 = 085 T2 = 160 T3 = T4 = 200 and λ = 003

Besides the center frequencies of the log-Gabor filters at four

scales were set as 16 112 124 and 148 These parameters

were then fixed for all the following experiments conducted

We take twenty set of database in which each database

consists of around seventy images Each and every image is

taken as the reference image and measured the similarity with

all other images present and the results are tabulated for FSIM

in Table I whereas for SSIM the results are tabulated in Table

II The average similarity index for each and every database

for the FSIM and SSIM are given in Figure 7 The results

clearly indicate that similarity measure is a good sign of a

quality measure as well as good metric to identify the

similarity between the images The results also gave a clear

indication that FSIM overcomes the drawbacks of SSIM and

gave a good measurement when compared to the SSIM

Fig 7 Graphical representation of FSIM and SSIM average values of the

given database

V CONCLUSION AND FUTURE WORK

The proposed work implemented the similarity index

assessment of thermal images following the sequence of the

work g iven as follows Darwinian Particle Swarm

Optimization is used for image segmentation as a multi-

threshold technique which has overcome various drawbacks

like computational time feature selectivity stability and

feasibility DPSO is better when compared to other

conventional multi-threshold techniques like Otsu image

segmentation fuzzy clustering PSO and ant colony

optimization Active contour image segmentation was

performed which is based on the level set based segmentation

method of Mumford Shah model producing binary image The

CORF operator extracts the contour image using Difference of

Gaussians and hysteresis thresholding The similarities of the

results are compared using FSIM and SSIM FSIM

outperforms the results of SSIM The results are good enough

to show that Image Quality Assessment techniques are helpful

in the process of identificat ion and classification of subjects

The given below points can be considered as a future work (i)

The results can be compared with other IQA metrics and (ii)

The proposed approach need to be explored in the domain of

medical imaging and satellite communicat ion

REFERENCES

[1] W Zhao R Chellappa A Rosenfeld and P Phillips ldquoFace recognition

A literature surveyrdquo ACM Computer Survey vol 35 no 4 pp 399-458 December 2003

[2] T Bourlai A Ross C Chen and L Hornak A study on using mid-wave infrared imagesfor face recognition In Proc SPIE 2012

[3] R S Ghiass O Arandjelovic A Bendada and X Maldague Infrared face recognition a literature review In Proc International Joint Conference on Neural Networks pages2791-2800 2013

[4] Yufeng Zheng ldquoFace detection and eyeglasses detection for thermal face recognitionrdquo ISampTSPIE Electronic Imaging Conference 22-26 January 2012 in Burlingame California United States

[5] F J Prokoski R B Riedel and J S Coffin ldquoIdentification of individuals by means of facial thermographyrdquo in Proceedings of The IEEE 1992 International Carnahan Conference on Security Technology Crime Countermeasures Atlanta GA USA 14-16 Oct pp 120-125 IEEE 1992

[6] Cutler R ldquoFace recognition using infrared images and eigenfacesrdquo httpciteseeristpsueducutler96facehtml April 1996 visited July 2007

[7] Socolinsky D Selinger A ldquoA comparative analysis of face recognition performance with visible and thermal infrared imageryrdquo Proceedings of the International Conference o Pattern Recognition (ICPR02) vol2 p 40217 Quebec Canada August 2002

[8] Socolinsky D Selinger A Neuheisel J ldquoFace recognition with visible and thermal infrared imageryrdquo Computer Vision amp Image Understanding vol 91 p 72-114 2003

50

60

70

80

90

100

1 3 5 7 9 11 13 15 17 19

FS

IM a

nd

SS

IM V

alu

es

Subject No

FSIM

SSIM

International Journal of Pure and Applied Mathematics Special Issue

142

[9] H-W Tzeng H-C Lee and M-Y Chen The design of isotherm face recognition technique based on nostril localization In Proc International Conference on System Science and Engineering pages 82-86 2011

[10] O Arandjelovic R I Hammoud and R Cipolla Thermal and re ectance based personal identification methodology in challenging variable illuminations Pattern Recognition 43(5)1801-1813 2010

[11] T Jin C Shouming X Xiuzhen and J Gu Eyes localization in an infrared image In Proc IEEE International Conference on Automation and Logistics (ICAL) pages 217-222 2009

[12] T Bourlai and Z Jafri Eye detection in the middle-wave infrared spectrum Towards recognition in the dark In Proc IEEE International Workshop on Information Forensic and Security (WIFS) pages 1-6 2011

[13] B Martinez X Binefa and M Pantic Facial component detection in thermal imagery In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 48-54 2010

[14] Chen X Jing Z Xiao G ldquoFuzzy fusion for face recognitionrdquo Proceedings of the International Conference on Fuzzy Systems and Knowledge Discovery (FSKD05) p 672- 675 Changsha China August 2005

[15] S Zhao and R Grigat An automatic face recognition system in the near infrared spectrum MLDM pages 437-444 2005

[16] T Elguebaly and N Bouguila ldquoA Bayesian method for infrared face recognitionrdquo Machine Vision Beyond Visible Spectrum 2011

[17] Y Yoshitomi T Miyaura S Tomita and S Kimura Face identification using thermalimage processing RO-MAN pages 374-379 1997

[18] S Li R Chu M Ao L Zhang and R He Highly accurate and fast face recognitionusing near infrared images In Proc IAPR International Conference on Biometricspages 151-158 2006

[19] H Maeng H-C Choi U Park S-W Lee and A K Jain NFRAD Near-infraredface recognition at a distance In Proc International Joint Conference on Biometrics(IJCB) pages 1-7 2011

[20] D Goswami C H Chan D Windridge and J Kittler Evaluation of face recognition system in heterogeneous environments (visible vs NIR) In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 2160-2167 2011

[21] A Srivastana and X Liu Statistical hypothesis pruning for recognizing faces from infrared images Image and Vision Computing 21(7)651-661 2003

[22] Z Xie SWu G Liu and Z Fang Infrared face recognition based on radiant energy and curvelet transformation In Proc International Conference on Information Assurance and Security (IAS) 2215-218 2009

[23] P Buddharaju I Pavlidis and P Tsiamyrtzis Pose-invariant physiological face recognition in the thermal infrared spectrum In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 53-60 2006

[24] P Buddharaju and I Pavlidis Physiological face recognition is coming of age In Proc IEEE Conference on Computer Vision and Pattern Recognition pages 128-135 2009

[25] T R Gault N Blumenthal A A Farag and T Starr Extraction of the superficial facial vasculature vital signs waveforms and rates using thermal imaging In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 1-8 2010

[26] A Seal M Nasipuri D Bhattacharjee and DK Basu Minutiae based thermal face recognition using blood perfusion data International Conference on Image Information Processing pages 1-4 2011

[27] S Cho L Wang and W J Ong Thermal imprint feature analysis for face recognitionISIE pages 1875-1880 2009

[28] R S Ghiass O Arandjelovic A Bendada and X Maldague Vesselness features and the inverse compositional AAM for robust face recognition using thermal IR In Proc AAAI Conference on Artificial Intelligence pages 357-364 2013

[29] S Wu Z Gu K A Chia and S H Ong Infrared facial recognition using modified blood perfusion ICICS pages 1-5 2007

[30] Z Xie S Wu G Liu and Z Fang Infrared face recognition method based on blood perfusion image and curvelet transformation In Proc

International Conference on Wavelet Analysis and Pattern Recognition pages 360-364 2009

[31] Kennedy J amp Eberhart R ldquoA new optimizer using particle swarm theoryrdquo in Proceedings of the IEEE sixth international symposium on micro machine andhuman science pp 39ndash43 1995

[32] Tillett J Rao T M Sahin F Rao R amp Brockport S (2005) Darwinian Particle Swarm Optimization In Proceedings of the 2nd Indian international conference onartificial intelligence (pp 1474ndash1487)

[33] Z Chenglin S Xuebin S Songlin and J Ting ldquoFault diagnosis of sensor by chaos particle swarm optimization algorithm and support vector machinerdquo Expert Systems with Applications vol 38 no 8 pp 9908ndash9912 2011

[34] P Ghamisi M S Couceiro J A Benediktsson and N M F Ferreira An Efficient Method for Segmentation of Images Based on Fractional Calculus and Natural Selection Expert Systems With Applications vol 39 no 16 pp 12407- 2417 Nov 2012

[35] P Ghamisi M S Couceiro F M L Martins and J A Benediktsson Multi-level Image Segmentation Based on Fractional-Order Darwinian Particle Swarm Optimization IEEE Transactions on Geoscience and Remote Sensing vol 52 no 5 pp 2382-2394 May 2014

[36] M S Couceiro N M F Ferreira and J A T Machado ldquoFractional order Darwinian particle swarm optimizationrdquo in proc Symp FSS Coimbra Portugal pp 4-5 Nov 2011

[37] P Ghamisi M S Couceiro and J A Benediktsson Classification of Hyperspectral Images with Binary Fractional Order Darwinian PSO and Random Forests in Proc SPIE Image and Signal Processing for Remote Sensing XIX 2013

[38] G Majumder and M K Bhowmik ldquoGabor-Fast ICA feature extraction for thermal face recognition using linear kernel support vector machinerdquo Computational Intelligence and Networks (CINE) 2015 International Conference on DOI 101109CINE201514 pp21 ndash 25 2015

[39] T Chan L Vese and Y Sandberg Active contours without edges for vector-valued images Journal of Visual Communications and Image Representation 11 no 2 (2000) pp 130-141

[40] D Mumford and J Shah Optimal approximation by piecewise smooth functions and associated variational problems Comm Pure Appl Math 42 1989 pp 577-685

[41] M Sussman P Smereka and S Osher A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow J Comput Phys V 119 (1994) pp 146-159

[42] L Vese and T Chan A multiphase level set framework for image segmentation using the mumford and shah model International Journal of Computer Vision vol 50 pp 271-293 2002

[43] T F Chan and L A Vese Image segmentation using level sets and the piecewise-constant Mumford-Shah model 2000

[44] D Cremers F R Schmidt and F Barthel Shape priors in variational image segmentation Convexity lipschitz continuity and globally optimal solutions in Computer Vision and Pattern Recognition 2008 CVPR 2008 IEEE Conference on 2008 pp 1-6

[45] S Osher and J A Sethian Fronts propagating with curvature-dependent speed algorithms based on Hamilton-Jacobi formulations Journal of computat ional physics vol 79 pp 12-49 1988

[46] R Ronfard Region-based strategies for active contour models International Journal of Computer Vision vol 13 pp 229-251 1994

[47] K Siddiqi Y B Lauziere A Tannenbaum and S W Zucker Area and length minimizing flows for shape segmentation Image Processing IEEE Transactions on vol 7 pp 433-443 1998

[48] Cosmin Grigorescu Nicolai Petkov Michel A Westenberg Contour and boundary detection improved by surround suppression of texture edges Image and Vision Computing Vol 22 pp 609-622 2004

[49] Azzopardi G Petkov N A CORF computational model of a simple cell that relies on LGN input outperforms the Gabor function model Biol Cybern 106(3) 177ndash189 (2012)

[50] Azzopardi G Petkov N Contour detection by CORF operator In Villa AEP Duch W Erdi P Masulli F Palm G (eds) ICANN 2012 Part I LNCS vol acute 7552 pp 395ndash402 Springer Heidelberg (2012)

International Journal of Pure and Applied Mathematics Special Issue

143

[51] Z Wang AC Bovik HR Sheikh and EP Simoncelli ldquoImage quality assessment from error visibility to structural similarityrdquo IEEE Trans Image Process vol 13 no 4 pp 600-612 Apr 2004

[52] Lin Zhang Lei Zhang Xuanqin Mou and David Zhang FSIM a feature similarity index for image quality assessment IEEE Transactions on Image Processing vol 20 no 8 pp 2378-2386 2011

[53] P Kovesi ldquoImage features from phase congruencyrdquo Videre J Comp Vis Res vol 1 no 3 pp 1-26 1999

[54] L Henriksson A Hyvaumlrinen and S Vanni ldquoRepresentation of cross-frequency spatial phase relationships in human visual cortexrdquo J Neuroscience vol 29 no 45 pp 14342-14351 Nov 2009

[55] C Mancas-Thillou and B Gosselin ldquoCharacter segmentation-by-recognition using log-Gabor filtersrdquo in Proc Int Conf Pattern Recognit 2006 pp 901-904

[56] S Fischer F Šroubek L Perrinet R Redondo and G Cristoacutebal ldquoSelf-invertible 2D log-Gabor waveletsrdquo Int J Computer Vision vol 75 no 2 pp 231-246 Nov 2007

[57] W Wang J Li F Huang and H Feng ldquoDesign and implementation of log-Gabor filter in fingerprint image enhancementrdquo Pattern Recognit Letters vol 29 no 3 pp 301-308 Feb 2008

[58] H R Sheikh and A C Bovik Image information and visual quality IEEE Trans Image Processing vol 15 pp 430-444 Feb 2006

[59] Z Wang Rate scalable foveated image and video communications PhD thesis Dept of ECE the University of Texas at Austin Dec 2001

[60] Z Wang and A C Bovik A universal image quality index IEEE Signal Processing Letters vol 9 pp 81-84 March 2002

International Journal of Pure and Applied Mathematics Special Issue

144

145

146

accuracy of 96 for frontal and semi-profile views and 100

accuracy rate for profile v iews and compared the results with

the visible images and achieved the promising results

Socolinsky et al [7] [8] used linear methods like Principal

Component Analysis (PCA) Linear Discriminant Analysis

(LDA) and Independent Component Analysis (ICA) and the

results reinforced the research methodologies in thermal facial

images and results were compared with visible face images

But in all the above mentioned survey some limitations were

applied like challenges in the data set less time lapse was

maintained no thermal image with glasses and pose or

expression were consideredIn the works of Tzeng et al [9]

Arandjelovic et al [10] Jin et al [11] Bourlai et al [12] and

Martinez et al [13] focussed on eyes localizat ion errors and

registration errors were reported

In Chen et al [14] work there was a considerable

reduction in the recognition rates of thermal facial images

when small localization errors were synthetically introduced to

manually marked eye positions Zhao et al [15] used active

Near Infrared data and solved the problem of localizing the

eyes in passively acquired images In this paperNIR lighting

source was placed and aligned with the camera axis is used to

illuminate the face Because the interior of the eyes reacts the

incident light the pupils appear distinctively bright and as such

are readily detected in the observed image (the so-called bright

pupil effect) Zhao et al used the locations of pupils to

register images of faces which are then represented using

their DCT coefficients and classified using a support vector

machineIn recent advances in appearance based methods

Elguebaly and Bouguila [16] described a method based on a

generalized Gaussian mixture model theparameters of which

are learnt from a training image set using a Bayesian approach

and achieved approximately 95 rank-1 rate

Feature based method is the second approach in the

infrared based face image segmentation An early method of

feature extraction method was proposed by Yoshitomi et al

[17] In this paper the approach of neural network with gray

level h istograms was combined and achieved a recognition

rate of 92 But the increase in temperature difference

between training and testing data decreased the rate of

detection Li et al [18] have done a lot of research in thermal

face image detectionusing local binary patterns The research

was done in closed environment and room temperatures and

the work resulted in good results But the drawback was that

the technique was unsuitable for outdoor environmental

conditions Maeng et al [19] also applied local binary patterns

in which the results were not efficient whereas SIFT (Scale-

Invariant Feature Transform) based features providing

impressive results Goswami et al [20] worked on variations of

local binary patterns and compared the results Wavelet

transform using Gabor filters were first implemented by

Srivastava et al [21] The results outperformed the holistic

based approaches of independent component analysis and

eigenfaces The curvelet transform is an extension of wavelet

transform which was first implemented by Xie et al [22] in the

infrared facial images and achieved increase in recognition

rate of 1-2 over other conventional wavelet transform

techniques Buddharaju et al [23][24] published first work on

vascular features followed by the contributions of Gault et al

[25]and Seal et al [26] The work of these authors extracted

blood vessels from thermal images using simple

morphological filters Cho et al [27] modified the approach of

Buddharaju et al on Equinox database and the results were

better and overtook Adaboost class ifiers mult ilayer

perceptron and Naiumlve Bayes classification The contribution

by Ghiass et al [28] were better than previous works on

vascular networks by applying Active Appearance Models on

pose variations and gave the proof of extracting the actual

blood vessels from vascular structures Wu et al [29] and Xie

et al [30] worked on blood perfusion model Wu et al took

the original segmented thermograms and the output images

were b lood perfusion image data were matched using RBF and

linear discriminant analysis where as Xie et al proposed a

model based on pennes equation whose results were better

than Wu et al

In our work a unique approach has been followed by the

segmentation fusion of PSO based image segmentation and

Active contour without edges In the second stage post

processing is done by CORF detector and the results are

matched with FSIM and SSIM

III PROPOSED WORK

The methodology of the proposed work is represented in

Figure 1

A DPSO based Image segmentation

Particle Swarm Optimization (PSO) is a random distribution

based search technique of Swarm Intelligence which involves

the movement of entities like school of birds or flock of fish

given by Kennedy and Eberhart [31] in 1995 PSO is also an

optimization technique or stochastic technique to find the best

solution among the given candidate solutions A simple

formulae is applied on particle‟s position and velocity There

are three variants of PSO in image segmentation which

includes (i) Darwinian Particle Swarm Optimizat ion ([32]

[33]) (ii) Fract ional-Order Darwinian Part icle Swarm

Optimization ([34] [35]) and (iii) Binary Fract ional Order

Darwin ian Part icle Swarm Opt imization [36]

International Journal of Pure and Applied Mathematics Special Issue

136

Fig 1 The proposed Sudheer-Sheela automatic thermal face detection framework using DPSO and Active Contour image segmentation

Enrichments were given to the original PSO by Tillett et al

[32] and developed a type of PSO technique called as

Darwin ian PSO which is implemented in this paper DPSO is

one of the variant of PSO in which number of swarms of test

solutions may exist at any time The performance of the each

individual swarm looks similar to an ordinary PSO algorithm

with some guidelines and rules that are designed and planned

to simulate natural selection This type of natural selection is

termed as Darwin ian principle of Survival of the fittest Each

swarm individually performs optimization just like a PSO

algorithm with some rules governing the collection of thermal

face image

The image segmentation procedure described in [37] is given here Let there be L intensity levels in each component

three color components for RGB images of a given image and these level are in the range 012hellip 119871 minus 1

119901119894119862 =

119893119894119862

119873 119901119894

119862 = 1119871 minus 1

119894 = 0 (1)

wherei represents a specific intensity level ie 0 le 119894 le 119871 minus1 C represents the component of the image 119862 = 119877119866 119861 for

RGB imagesN represents the total number of pixels in the image and 119893119894

119862 denotes the number of pixels for the

corresponding intensity levels i in component C or 119893119894119862

represents an image histogram for each component C which can be normalized and regarded as the probability

distribution119901119894119862 The total mean of each component of the

image can be easily calculated as

120583119879119862 = 119894119901119894

119862 = 1119871 minus 1

119894 = 0 (2)

The probabilit ies of occurrence 119908119895119862 of classes 1198631

119862hellip 119863119899119862

are given by

119908119895119862 =

119901119894

119862 119905119895119862

119894 = 0 119895 = 1

119901119894119862

119905119895119862

119894 = 119905119895 minus 1119862 + 1

1 lt 119895 lt 119899

119901119894119862

119871 minus 1

119894 = 119905119895 minus 1119862 + 1

119895 = 119899

(3)

The mean of each class 120583119895119862 can then be calculated as

120583119895119862 =

119901119894119862

119908119895119862 119902

119905119895119862

119894 = 0 119895 = 1

119901119894119862

119908119895119862

119905119895119862

119894 = 119905119895 minus 1119862 + 1

1 lt 119895 lt 119899

119901119894119862

119908119895119862 119871 minus 1

119894 = 119905119895 minus 1119862 + 1

119895 = 119899

(4)

The simplest and computationally most efficient method of obtaining the optimal threshold is the one that maximizes the

between-class variance of each component which can be generally defined by

1205901198611198622

= 119908119895119862 120583119895

119862 minus 120583119879119862

2119899119895 = 1 (5)

wherei represents a specific class in such a way that 119908119895119862 and

120583119895119862 are the probability of occurrence and the mean of class j

respectivelyThe problem of n-level thresholding is reduced to

an optimization problem to search for the thresholds 119905119895119862 that

International Journal of Pure and Applied Mathematics Special Issue

137

maximize the objective functions (ie fitness function) of

each image component C generally given in equation 6 and the model results are displayed in Figure 2

120593119862 = max

1lt1199051119862 lt⋯lt119871minus1

1205901198611198622

119905119895119862 (6)

Fig 2 (a) Thermal images and (b) DPSO segmented images

B Active Contour Image Segmentation

Image segmentation is a central task in solving the region of

interest problem in image processing In general there are

three conventional methods of image segmentation procedures

like pixel based methods region based methods and edge

based methods all of which depends the local information of

the image [38] In our paper hybrid approach to image

segmentation is introduced named as Active contours without

edges [39][40] helps to find object boundary in a given image

based on curve evolution technique [41][42] popularly known

as level set method The basic impression of the level set

method or any active contour method is to evolve a curve over

time so that the curve moves towards its interiornormal and

when the stopping conditions are met the curve forms an

outline around theobject of interest For a g iven image 119868 [43]

we can create a level set function empty 119909 119910 withthe same size o f

the image 119868to describe the contour The contour is defined as

the zerolevel set of the function emptyas given in equation 7

119862 = 119909 119910 119891 119909 119910 = 0 (7)

(i) Energy Equation

The evolution of the initial contour is guided by an energy equation For the contour with an Signed Distance Function

(SDF) (empty119888 119909 119910 ) the energy function can be expressed as

119864 119862 = 119864 empty119888 119909 119910 = 1199081119864119868119898119886119892119890 119862 + 1199082119864119878119893119886119901119890 119862 +

1199083119864119877119890119892119906119897119886119903119894119911119886119905119894119900119899 119862 (8)

Where1199081 1199082and 1199083are real valued positive constant

weighting factors The image term119864119868119898119886119892119890 119862 attracts the

contour towards the object boundary 119864119878119893119886119901119890 119862 the shape

term penalizes the curve for deviating from uniformlayer

thickness [44] Lastly the regularizat ion

term119864119877119890119892119906119897119886119903119894119911119886119905119894119900119899 119862 helps to create a min imal length

smooth contour [45]Based on the combination of these energy

equation components (empty119888 119909 119910 ) is deformed to min imize

(empty119888 119909 119910 119905 )

(ii) Image term

119864119868119898119886119892119890 119862 =

1205821 119868 119909 119910 minus 1198881 2119889119909119889119910

119903119890119892119894119900119899 119887119890119905119908119890119890119899 119862119894 119886119899119889 119862119894minus1

+ 1205822 119868 119909 119910 minus 1198882 2

119903119890119892119894119900119899 119887119890119905119908119890119890119899 119862119894 119886119899119889 119862119894+1119889119909119889119910(9)

The image term divides the image into regions inside and

outside of the contour 119862 The values 1198621and 1198622are the values

of the mean pixel intensity inside and outside of the contour

respectively The constants 1205821and1205822are constants typically

both set to 1 This term reaches a minimum when the contour

divides the area inside and outside in regions of constant

homogeneity ie when lies along an object boundary [46]

Using the level set formulation the image term can be

expressed as

119864119868119898119886119892119890 = 1205821 119868 119909 119910 minus 1198881 2119867 empty119894 minus 1 119909 119910 1

minus 119867 empty119894 119909119910 119889119909119889119910

+ 1205822 119868 119909 119910 minus 1198882 2119867 empty119894 119909119910 1 minus 119867 empty119894+ 1 119909119910 119889119909119889119910

(10)

Where

119867 empty119894 minus 1 119909119910 1minus 119867 empty119894 119909119910 119886119899119889 119867 empty119894 119909 119910 1 minus

119867 empty119894+ 1 119909119910 are used to select the regions inside and

outside respectively

(iii) Shape term

The shape term is to say that each layer should be parallel to

the layer immediately above it Thus the shape term was

designed to penalize movement away from consistent

distances between boundaries For the boundary the boundary

is used for comparison The shape term is expressed by

119864119878119893119886119901119890 119862119894

= 119898119886119909 0 119862119894 119909 minus119862119894 minus 1 119909 minus 119880119894 119862119894 119909 minus 119862119894 minus 1 119909 minus119909119871119894 119889119909 (11)

Using the level set formulation the shape force term becomes

119864119868119898119886119892119890 empty119894 119909119910 = 119898119886119909 0 119910 minus119862119894 minus 1 119909 minus119880119894 119910 minus

119862119894 minus 1 119909 minus 119871119894 120575 empty119894 119909 119910 |nablaempty119894 119909 119910 |119889119909119889119910

(12)

Where120575 empty119894 119909 119910 |nablaempty119894 119909 119910 |is used to select the current

boundary region

(iv) Regularization term

International Journal of Pure and Applied Mathematics Special Issue

138

The last term in the regularizat ion is used to encourage

smooth short contours [47] The force term can be expressed

simply as

119864119877119890119892119906119897119886119903119894119911119886119905119894119900119899 empty119894 119909119910 = 120575 empty119894 119909119910 |nablaempty119894 119909119910 |119889119909119889119910 (13)

The results of the active contour image segmentation are

displayed in Figure 3 and histogram representations are given

in Figure 4

Fig 3 Top row DPSO segmented images Bottom row Active contour

segmented images

Fig 4 (a) Thermal image(b) Histogram representation of thermal image (c) DPSO segmented image (d) DPSO segmented histogram representation (e) Active contour segmented image (f) Histogram of Active contour image

C CORF edge detector

The implementation of the proposed CORF operator is rather

straightforward it includes blurring (achieved by convolving

with a Gaussian function) of halfwave rectified responses of

DoG operators shifting appropriately these blurred res ponses

by different vectors which are determined in the configuration

of the operator and using them for the pixel-wise evaluation

of a weighted geometric mean that gives the output of the

CORF operatorWe apply a classical two-step procedure in

computer vision thatwas proposed by [48] and [49] to obtain a

binary contour mapfrom the output of the concerned model

The first step consists ofedge thinning by non-maximum

suppression to determine theridges in the given response

image Then we apply hysteresis thresholding to obtain a

binary contour map The latter steprequires a high and a low

threshold value Similar to the work in[50] we set the low

threshold value to a fraction (05) of the highthreshold For a

given image we set the high threshold to be thelowest value

of the strongest f pixels in the thinned responseimage The

given value of the parameter f is a fraction of the totalnumber

of pixels in the image The resulting binary map containsthe

strongest fraction f of contour pixels together with

anyconnected ones that are achieved by hysteresis

thresholding The parameters used for the CORF operator are

the number of orientations nϴ (n=12 for ϴ=П6) a scale

parameter σ wavelength λ= σ4 and a spatial aspect ratio

γ=05

(i) Non-maximum suppression edge thinning

TheNon-maxima suppression thins the areas in which

119862120590 119909 119910 is non-zero to one-pixel wide candidate contours as

follows For each position 119909 119910 two responses Cσ(x|y

|) and

Cσ(x||y

||) in adjacent positions (x

|y

|) and (x

||y

||) that are

intersection points of a line passing through 119909 119910 in

orientation 120579120590 119909 119910 and a square defined by the diagonal

points of an 8-neighbourhood are computed by linear

interpolation as given by Figure 5 If the response

119862120590 119909 119910 at 119909 119910 is greater than both these values (ie it is a

local maximumalong the concerned line) it is retained

otherwise it isassigned the value zero

Fig 5 Interpolated responses at positions (x|y

|) and (x

||y

||) Non-

maximasuppression retains the value in the central pixel ethx yTHORN if it is larger

than thevalues at (x|y

|) and (x

||y

||)

Fig 6 (a) Image after active contour segmentation (b) One pixel binarized hysteresis threshold image (c) Image after CORF edge detection

International Journal of Pure and Applied Mathematics Special Issue

139

ii) Binarizat ion by Hysteresis thresholding

Next a binary map is computed from the candidate contour

pixels by hysteresis thresholding This process involves two

threshold values TLand TH TLltTH Commonly the high

threshold value THis computed as a (1-p)-quantile of the

distribution of the response values at the candidate contour

pixels where p is the minimum fraction of candidate pixels to

be retained in the contour map Candidate contour pixels with

responses higher than th are definitely retained in the contour

map while the ones with responses below the low threshold

TLare discarded Candidate contour pixels with responses

between TLand THare retained if they can be connected to any

candidate contour pixel with a response higher than THthrough

a chain of other candidate contour pixels with responses larger

than TL Figure 6 gives the results of edge thinning by non-

maximum suppression to one pixel and CORF edge detection

by hysteresis thresholding

D FSIM and SSIM

The aim of objective Image Quality Assessment (IQA) is to

develop mathemat ical models that are able to forecast the

quality of an image precisely and spontaneously An ideal

objective IQA method should be able to simulate the quality

predictions of an average human observer The proper IQA

method calculates the similarity index using a mathemat ical

model by quantizing the distortion image and the reference

image The main feature of the proper IQA is that it can be

embedded in real t ime image processing system The most

advanced method to perform IQA is Structure Similarity Index

Measurement (SSIM) [51] The various features like

luminance contrast and structure are compared in the SSIM

Almost all these features are consistent with the Human

Visual System (HVS) and are compatible But there are few

drawbacks as the luminance and contrast are sensitive to the

illumination To overcome the drawbacks of the

aforementioned technique Feature Similarity Index

Measurement (FSIM) has come into existence [52] In FSIM

two features main ly Phase Congruency (PC) [53] [54] and

Gradient Magnitude (GM) are considered To compute the PC

of 2D grayscale images The 1D log-Gabor filters described

earlier can be extended to 2D ones by simply applying some

spreading function across thefilter perpendicular to its

orientation One widely used spreading functionis Gaussian

[55] [56] and [57] By using Gaussian as the spreading

function the 2D log-Gabor function has the following transfer

function

1198662 120596120579119895 = 119890119909119901 119897119900119892 120596 1205960

2

21205901199032

119890119909119901 120579minus120579119895

2

21205901205792

(14)

Where 120579119895 = 119895120587 119869 119895 = 01hellip 119869 minus 1 the orientation angle of

the filter is 119869 is the number of orientations and 120590120579determines

the filter‟s angular bandwidthBy modulat ing 120596120579 and 120579119895 and

convolving 1198662with the 2D image we get a set of responses at

each point x as 119890119899120579119895 119883 119874119899 120579119895

119883 The local amplitude on

scale n and orientation 120579119895is119860119899120579119895 119883 = 119890119899 120579119895

119883 2 +119874119899 120579119895 119883 2

and the local energy along orientation 120579119895 is119864120579119895 119883 =

119865120579119895 119883 2 + 119867120579119895

119883 2 where119865120579119895 119883 = 119890119899 120579119895

119883 119899 and

119867120579119895 119883 = 119900119899 120579119895

119883 119899 The 2D PC at x is defined as

1198751198622119863 119883 = 119864120579 119895

119883 119895

휀+ 119860119899 120579 119895 119883 119895119899

(15)

It should be noted that 1198751198622119863 119883 is a real number within 0~1

(i) The FS IM index

The computation of FSIM index consists of two stages In the

first stage the local similarity map is computed and then in

the second stage we pool the similarity map into a single

similarity score We separate the feature similarity

measurement between 1198911 119883 and 1198912 119883 into two

components each for PC or GM First the similarity measure

for 1198751198621 119883 and 1198751198622 119883 is defined as

119878119875119862 119883 =21198751198621 119883 1198751198622 119883 +1198791

11987511986212 119883 +1198751198622

2 119883 +1198791 (16)

where 1198791 is a positive constant to increase the stability of SPC

(such a consideration was also included in SSIM [51]) In practice the determination of 1198791 depends on the dynamic

range of PC values Equation 16 is a commonly used measure

to define the similarity of two positive real numbers and its

result ranges within [0 1] Similarly the GM values 1198661 119883

and 1198662 119883 are compared and the similarity measure is defined

as

119878119866 119883 =21198661 119883 1198662 119883 +1198792

11986612 119883 +1198662

2 119883 +1198792 (17)

where 1198792 is a positive constant depending on the dynamic

range of GM values In our experiments both 1198791 and 1198792 will

be fixed to all databases so that the proposed FSIM can be conveniently used Then 119878119875119862 119883 and 119878119866 119883 are combined to

get the similarity 119878119871 119883 of 1198911 119883 and 1198912 119883 We define

119878119871 119883 as

119878119871 119883 = 119878119875119862 119883 120572

119878119866 119883 120573

(18)

where 120572 and 120573 are parameters used to adjust the relative

importance of PC and GM features In this paper we set 120572 = 120573 =1 for simplicity Thus119878119871 119883 = 119878119875119862 119883 119878119866 119883 Having

obtained the similarity 119878119871 119883 at each location 119883 the overall

similarity between 1198911and 1198912 can becalculated However

different locations have different contributions to HVS‟

perception of the image For example edge locations convey

more crucial v isual information than the locations within a

smooth area Since human visual cortex is sensitive to phase

congruent structures [54] the PC value at a location canreflect

how likely it is a perceptibly significant structure point Intuitively for a given location 119883 if anyone of 1198911 119883 and

1198912 119883 has a significant PC value it implies that this position x

International Journal of Pure and Applied Mathematics Special Issue

140

will have a high impact on HVS in evaluating the similarity between 1198911 and 1198912 Therefore we use 119875119862119898 119883 =

max(1198751198621 119883 1198751198622 119883 ) to weight the importance of 119878119871 119883 in

the overall similarity between 1198911 and 1198912 and accordingly the

FSIM index between 1198911and 1198912 is defined as

119865119878119868119872 = 119878119871 119883 119883 isinΩ 119875119862119898 119883

119875119862119898 119883 119883isinΩ (19)

where Ω means the whole image spatial domain

(ii) Structural similarity index (SSIM)

The SSIM algorithm performs similarity measurement in three

steps luminance comparison contrast comparison and

structure comparison First the luminance of each image

signal is compared The estimated mean intensity is computed

as follows

120583119903119890119891 =1

119882119867 119868119903119890119891 119894 119895

119882119894 = 1

119867119895 = 1 (20)

The luminance comparison function 119897 119868119903119890119891 119868119905119904119905 is a

function of 120583119903119890119891 and 120583119905119904119905Second the contrast of each image

signal is compared For estimat ing the contrast standard

deviation is being used An unbiased estimate of standard

deviation in discrete form is as follows 120590119903119890119891

= 1

119882119867minus1 119868119903119890119891 119894 119895 minus 120583119903119890119891

2119882119894 = 1

119867119895 = 1

1

2

(21)

The contrast comparison function 119888 119868119903119890119891 119868119905119904119905 is a function

of120590119903119890119891 and 120590119905119904119905 Third the structure of each image signal is

compared Structure comparison function119904 119868119903119890119891 119868119905119904119905 is a

function of 119868119903119890119891 minus 120583119903119890119891 120590119903119890119891 and

119868119905119904119905 minus 120583119905119904119905 120590119905119904119905 Finally three comparison functions are

combined and an overall similarity measure is produced The

overall similarity measure119878 119868119903119890119891 119868119905119904119905 is a function of

119897 119868119903119890119891 119868119905119904119905 119888 119868119903119890119891 119868119905119904119905 119888 119868119903119890119891 119868119905119904119905 and 119904 119868119903119890119891 119868119905119904119905

Definitions of119897 119868119903119890119891 119868119905119904119905 119888 119868119903119890119891 119868119905119904119905 and119904 119868119903119890119891 119868119905119904119905 are as

follows

For luminance comparison function we have

119904 119868119903119890119891 119868119905119904119905 =2120583119903119890119891 120583119905119904119905 +1198791

1205831199031198901198912 +120583119905119904119905

2 +1198791 (21)

where 1198791 is a positive stabilizing constant chosen to prevent

the denominator from becoming too small We have

1198791 = 1199051119863 2 (22)

where D is the dynamic range of pixel values and 1199051 ltlt 1 is

a small constant For contrast comparison function we have

119888 119868119903119890119891 119868119905119904119905 =2120590119903119890119891 120590119905119904119905 +1198792

1205901199031198901198912 +120590119905119904119905

2 +1198792 (23)

where 1198792 = 1199052119863 2is a positive stabilizing constant

And1199052 ltlt 1 For structure comparison function we have

119904 119868119903119890119891 119868119905119904119905 =120590119903119890119891 119905119904119905+1198793

120590119903119890119891 120590119905119904119905 +1198793 (24)

where 1198793 is a positive stabilizing constant In (58)120590119903119890119891 119905119904119905 is

the correlation coefficient between the reference and test images In the discrete form120590119903119890119891 119905119904119905 can be estimated by

120590119903119890119891 119905119904119905 =1

119882119867minus1 119868119903119890119891 119894 119895 minus 120583119903119890119891 119868119905119904119905 119894 119895 minus

119882119894 = 1

119867119895 = 1

120583119905119904119905 (25)

Finally structural similarity index is defined as

119878119878119868119872 119868119903119890119891 119868119905119904119905 =

119897 119868119903119890119891 119868119905119904119905 120572 119888 119868119903119890119891 119868119905119904119905

120573 119904 119868119903119890119891 119868119905119904119905

120574 (26)

where 120572 120573 and 120574The universal quality index (UQI) [5960] is a special case of the SSIM index when1198791 = 1198792 = 1198793 = 0

and 120572 = 120573 = 120574 = 1 Since image statistical features and

distortions are usually space-variant authors of [60] employ

the SSIM index locally instead of globally Another reason for

this is that by applying the SSIM index locally a quality map

of the image which conveys more information about the

quality degradation can be generated

TABLE I SAMPLE TEN SUBJECT‟S FSIM VALUES WITH RESPECT TO EACH OTHER

Subject No

11 12 13 14 15 16 17 18 19 20

11 9342 7906 7438 7442 7648 7566 7509 78 7441 7597

12 7906 9523 734 7135 7459 745 7394 7505 7335 7449

13 7438 734 9705 743 7943 7264 776 7417 7941 7735

14 7442 7135 743 9429 8081 7252 7428 7478 7604 7406

15 7648 7459 7943 8081 943 7734 818 7903 834 8126

16 7566 745 7264 7252 7734 9247 7599 8769 7523 7713

17 7509 7394 776 7428 8189 7599 934 7552 8102 8612

18 7801 7505 7417 7478 7903 8769 7552 9342 7631 7669

19 7441 7335 7941 7604 834 7523 8102 7631 9693 806

20 7597 7449 7735 7464 8126 7713 8612 7669 806 9479

International Journal of Pure and Applied Mathematics Special Issue

141

TABLE II SAMPLE TEN SUBJECT‟S SSIM VALUES WITH RESPECT TO EACH OTHER

Subject No

11 12 13 14 15 16 17 18 19 20

11 9044 7333 6507 6937 7054 7217 6717 7433 6588 6854

12 7333 9327 6249 6298 6574 6905 6357 6976 6258 6421

13 6507 6249 9643 6744 7311 6586 7173 671 7242 7014

14 6937 6298 6744 9155 7673 6857 6911 7007 7009 6874

15 7054 6574 7311 7673 9158 7325 7676 7475 7685 7621

16 7217 6905 6586 6857 7325 925 711 867 694 7189

17 6717 6357 7173 6911 7676 711 9147 7083 7443 822

18 7433 6976 671 7007 7475 867 7083 9236 7054 7145

19 6588 6258 7242 7009 7685 694 7443 7054 9495 7423

20 6854 6421 7014 6874 7621 7189 822 7145 7423 9251

IV EXPERIMENTAL RESULTS AND ANALYSIS

In this section the performance of IQA techniques like FSIM

and SSIM are evaluated The parameters required in the

proposed methods were set as n = 4 J = 4 σr = 05978 σθ =

06545 T1 = 085 T2 = 160 T3 = T4 = 200 and λ = 003

Besides the center frequencies of the log-Gabor filters at four

scales were set as 16 112 124 and 148 These parameters

were then fixed for all the following experiments conducted

We take twenty set of database in which each database

consists of around seventy images Each and every image is

taken as the reference image and measured the similarity with

all other images present and the results are tabulated for FSIM

in Table I whereas for SSIM the results are tabulated in Table

II The average similarity index for each and every database

for the FSIM and SSIM are given in Figure 7 The results

clearly indicate that similarity measure is a good sign of a

quality measure as well as good metric to identify the

similarity between the images The results also gave a clear

indication that FSIM overcomes the drawbacks of SSIM and

gave a good measurement when compared to the SSIM

Fig 7 Graphical representation of FSIM and SSIM average values of the

given database

V CONCLUSION AND FUTURE WORK

The proposed work implemented the similarity index

assessment of thermal images following the sequence of the

work g iven as follows Darwinian Particle Swarm

Optimization is used for image segmentation as a multi-

threshold technique which has overcome various drawbacks

like computational time feature selectivity stability and

feasibility DPSO is better when compared to other

conventional multi-threshold techniques like Otsu image

segmentation fuzzy clustering PSO and ant colony

optimization Active contour image segmentation was

performed which is based on the level set based segmentation

method of Mumford Shah model producing binary image The

CORF operator extracts the contour image using Difference of

Gaussians and hysteresis thresholding The similarities of the

results are compared using FSIM and SSIM FSIM

outperforms the results of SSIM The results are good enough

to show that Image Quality Assessment techniques are helpful

in the process of identificat ion and classification of subjects

The given below points can be considered as a future work (i)

The results can be compared with other IQA metrics and (ii)

The proposed approach need to be explored in the domain of

medical imaging and satellite communicat ion

REFERENCES

[1] W Zhao R Chellappa A Rosenfeld and P Phillips ldquoFace recognition

A literature surveyrdquo ACM Computer Survey vol 35 no 4 pp 399-458 December 2003

[2] T Bourlai A Ross C Chen and L Hornak A study on using mid-wave infrared imagesfor face recognition In Proc SPIE 2012

[3] R S Ghiass O Arandjelovic A Bendada and X Maldague Infrared face recognition a literature review In Proc International Joint Conference on Neural Networks pages2791-2800 2013

[4] Yufeng Zheng ldquoFace detection and eyeglasses detection for thermal face recognitionrdquo ISampTSPIE Electronic Imaging Conference 22-26 January 2012 in Burlingame California United States

[5] F J Prokoski R B Riedel and J S Coffin ldquoIdentification of individuals by means of facial thermographyrdquo in Proceedings of The IEEE 1992 International Carnahan Conference on Security Technology Crime Countermeasures Atlanta GA USA 14-16 Oct pp 120-125 IEEE 1992

[6] Cutler R ldquoFace recognition using infrared images and eigenfacesrdquo httpciteseeristpsueducutler96facehtml April 1996 visited July 2007

[7] Socolinsky D Selinger A ldquoA comparative analysis of face recognition performance with visible and thermal infrared imageryrdquo Proceedings of the International Conference o Pattern Recognition (ICPR02) vol2 p 40217 Quebec Canada August 2002

[8] Socolinsky D Selinger A Neuheisel J ldquoFace recognition with visible and thermal infrared imageryrdquo Computer Vision amp Image Understanding vol 91 p 72-114 2003

50

60

70

80

90

100

1 3 5 7 9 11 13 15 17 19

FS

IM a

nd

SS

IM V

alu

es

Subject No

FSIM

SSIM

International Journal of Pure and Applied Mathematics Special Issue

142

[9] H-W Tzeng H-C Lee and M-Y Chen The design of isotherm face recognition technique based on nostril localization In Proc International Conference on System Science and Engineering pages 82-86 2011

[10] O Arandjelovic R I Hammoud and R Cipolla Thermal and re ectance based personal identification methodology in challenging variable illuminations Pattern Recognition 43(5)1801-1813 2010

[11] T Jin C Shouming X Xiuzhen and J Gu Eyes localization in an infrared image In Proc IEEE International Conference on Automation and Logistics (ICAL) pages 217-222 2009

[12] T Bourlai and Z Jafri Eye detection in the middle-wave infrared spectrum Towards recognition in the dark In Proc IEEE International Workshop on Information Forensic and Security (WIFS) pages 1-6 2011

[13] B Martinez X Binefa and M Pantic Facial component detection in thermal imagery In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 48-54 2010

[14] Chen X Jing Z Xiao G ldquoFuzzy fusion for face recognitionrdquo Proceedings of the International Conference on Fuzzy Systems and Knowledge Discovery (FSKD05) p 672- 675 Changsha China August 2005

[15] S Zhao and R Grigat An automatic face recognition system in the near infrared spectrum MLDM pages 437-444 2005

[16] T Elguebaly and N Bouguila ldquoA Bayesian method for infrared face recognitionrdquo Machine Vision Beyond Visible Spectrum 2011

[17] Y Yoshitomi T Miyaura S Tomita and S Kimura Face identification using thermalimage processing RO-MAN pages 374-379 1997

[18] S Li R Chu M Ao L Zhang and R He Highly accurate and fast face recognitionusing near infrared images In Proc IAPR International Conference on Biometricspages 151-158 2006

[19] H Maeng H-C Choi U Park S-W Lee and A K Jain NFRAD Near-infraredface recognition at a distance In Proc International Joint Conference on Biometrics(IJCB) pages 1-7 2011

[20] D Goswami C H Chan D Windridge and J Kittler Evaluation of face recognition system in heterogeneous environments (visible vs NIR) In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 2160-2167 2011

[21] A Srivastana and X Liu Statistical hypothesis pruning for recognizing faces from infrared images Image and Vision Computing 21(7)651-661 2003

[22] Z Xie SWu G Liu and Z Fang Infrared face recognition based on radiant energy and curvelet transformation In Proc International Conference on Information Assurance and Security (IAS) 2215-218 2009

[23] P Buddharaju I Pavlidis and P Tsiamyrtzis Pose-invariant physiological face recognition in the thermal infrared spectrum In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 53-60 2006

[24] P Buddharaju and I Pavlidis Physiological face recognition is coming of age In Proc IEEE Conference on Computer Vision and Pattern Recognition pages 128-135 2009

[25] T R Gault N Blumenthal A A Farag and T Starr Extraction of the superficial facial vasculature vital signs waveforms and rates using thermal imaging In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 1-8 2010

[26] A Seal M Nasipuri D Bhattacharjee and DK Basu Minutiae based thermal face recognition using blood perfusion data International Conference on Image Information Processing pages 1-4 2011

[27] S Cho L Wang and W J Ong Thermal imprint feature analysis for face recognitionISIE pages 1875-1880 2009

[28] R S Ghiass O Arandjelovic A Bendada and X Maldague Vesselness features and the inverse compositional AAM for robust face recognition using thermal IR In Proc AAAI Conference on Artificial Intelligence pages 357-364 2013

[29] S Wu Z Gu K A Chia and S H Ong Infrared facial recognition using modified blood perfusion ICICS pages 1-5 2007

[30] Z Xie S Wu G Liu and Z Fang Infrared face recognition method based on blood perfusion image and curvelet transformation In Proc

International Conference on Wavelet Analysis and Pattern Recognition pages 360-364 2009

[31] Kennedy J amp Eberhart R ldquoA new optimizer using particle swarm theoryrdquo in Proceedings of the IEEE sixth international symposium on micro machine andhuman science pp 39ndash43 1995

[32] Tillett J Rao T M Sahin F Rao R amp Brockport S (2005) Darwinian Particle Swarm Optimization In Proceedings of the 2nd Indian international conference onartificial intelligence (pp 1474ndash1487)

[33] Z Chenglin S Xuebin S Songlin and J Ting ldquoFault diagnosis of sensor by chaos particle swarm optimization algorithm and support vector machinerdquo Expert Systems with Applications vol 38 no 8 pp 9908ndash9912 2011

[34] P Ghamisi M S Couceiro J A Benediktsson and N M F Ferreira An Efficient Method for Segmentation of Images Based on Fractional Calculus and Natural Selection Expert Systems With Applications vol 39 no 16 pp 12407- 2417 Nov 2012

[35] P Ghamisi M S Couceiro F M L Martins and J A Benediktsson Multi-level Image Segmentation Based on Fractional-Order Darwinian Particle Swarm Optimization IEEE Transactions on Geoscience and Remote Sensing vol 52 no 5 pp 2382-2394 May 2014

[36] M S Couceiro N M F Ferreira and J A T Machado ldquoFractional order Darwinian particle swarm optimizationrdquo in proc Symp FSS Coimbra Portugal pp 4-5 Nov 2011

[37] P Ghamisi M S Couceiro and J A Benediktsson Classification of Hyperspectral Images with Binary Fractional Order Darwinian PSO and Random Forests in Proc SPIE Image and Signal Processing for Remote Sensing XIX 2013

[38] G Majumder and M K Bhowmik ldquoGabor-Fast ICA feature extraction for thermal face recognition using linear kernel support vector machinerdquo Computational Intelligence and Networks (CINE) 2015 International Conference on DOI 101109CINE201514 pp21 ndash 25 2015

[39] T Chan L Vese and Y Sandberg Active contours without edges for vector-valued images Journal of Visual Communications and Image Representation 11 no 2 (2000) pp 130-141

[40] D Mumford and J Shah Optimal approximation by piecewise smooth functions and associated variational problems Comm Pure Appl Math 42 1989 pp 577-685

[41] M Sussman P Smereka and S Osher A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow J Comput Phys V 119 (1994) pp 146-159

[42] L Vese and T Chan A multiphase level set framework for image segmentation using the mumford and shah model International Journal of Computer Vision vol 50 pp 271-293 2002

[43] T F Chan and L A Vese Image segmentation using level sets and the piecewise-constant Mumford-Shah model 2000

[44] D Cremers F R Schmidt and F Barthel Shape priors in variational image segmentation Convexity lipschitz continuity and globally optimal solutions in Computer Vision and Pattern Recognition 2008 CVPR 2008 IEEE Conference on 2008 pp 1-6

[45] S Osher and J A Sethian Fronts propagating with curvature-dependent speed algorithms based on Hamilton-Jacobi formulations Journal of computat ional physics vol 79 pp 12-49 1988

[46] R Ronfard Region-based strategies for active contour models International Journal of Computer Vision vol 13 pp 229-251 1994

[47] K Siddiqi Y B Lauziere A Tannenbaum and S W Zucker Area and length minimizing flows for shape segmentation Image Processing IEEE Transactions on vol 7 pp 433-443 1998

[48] Cosmin Grigorescu Nicolai Petkov Michel A Westenberg Contour and boundary detection improved by surround suppression of texture edges Image and Vision Computing Vol 22 pp 609-622 2004

[49] Azzopardi G Petkov N A CORF computational model of a simple cell that relies on LGN input outperforms the Gabor function model Biol Cybern 106(3) 177ndash189 (2012)

[50] Azzopardi G Petkov N Contour detection by CORF operator In Villa AEP Duch W Erdi P Masulli F Palm G (eds) ICANN 2012 Part I LNCS vol acute 7552 pp 395ndash402 Springer Heidelberg (2012)

International Journal of Pure and Applied Mathematics Special Issue

143

[51] Z Wang AC Bovik HR Sheikh and EP Simoncelli ldquoImage quality assessment from error visibility to structural similarityrdquo IEEE Trans Image Process vol 13 no 4 pp 600-612 Apr 2004

[52] Lin Zhang Lei Zhang Xuanqin Mou and David Zhang FSIM a feature similarity index for image quality assessment IEEE Transactions on Image Processing vol 20 no 8 pp 2378-2386 2011

[53] P Kovesi ldquoImage features from phase congruencyrdquo Videre J Comp Vis Res vol 1 no 3 pp 1-26 1999

[54] L Henriksson A Hyvaumlrinen and S Vanni ldquoRepresentation of cross-frequency spatial phase relationships in human visual cortexrdquo J Neuroscience vol 29 no 45 pp 14342-14351 Nov 2009

[55] C Mancas-Thillou and B Gosselin ldquoCharacter segmentation-by-recognition using log-Gabor filtersrdquo in Proc Int Conf Pattern Recognit 2006 pp 901-904

[56] S Fischer F Šroubek L Perrinet R Redondo and G Cristoacutebal ldquoSelf-invertible 2D log-Gabor waveletsrdquo Int J Computer Vision vol 75 no 2 pp 231-246 Nov 2007

[57] W Wang J Li F Huang and H Feng ldquoDesign and implementation of log-Gabor filter in fingerprint image enhancementrdquo Pattern Recognit Letters vol 29 no 3 pp 301-308 Feb 2008

[58] H R Sheikh and A C Bovik Image information and visual quality IEEE Trans Image Processing vol 15 pp 430-444 Feb 2006

[59] Z Wang Rate scalable foveated image and video communications PhD thesis Dept of ECE the University of Texas at Austin Dec 2001

[60] Z Wang and A C Bovik A universal image quality index IEEE Signal Processing Letters vol 9 pp 81-84 March 2002

International Journal of Pure and Applied Mathematics Special Issue

144

145

146

Fig 1 The proposed Sudheer-Sheela automatic thermal face detection framework using DPSO and Active Contour image segmentation

Enrichments were given to the original PSO by Tillett et al

[32] and developed a type of PSO technique called as

Darwin ian PSO which is implemented in this paper DPSO is

one of the variant of PSO in which number of swarms of test

solutions may exist at any time The performance of the each

individual swarm looks similar to an ordinary PSO algorithm

with some guidelines and rules that are designed and planned

to simulate natural selection This type of natural selection is

termed as Darwin ian principle of Survival of the fittest Each

swarm individually performs optimization just like a PSO

algorithm with some rules governing the collection of thermal

face image

The image segmentation procedure described in [37] is given here Let there be L intensity levels in each component

three color components for RGB images of a given image and these level are in the range 012hellip 119871 minus 1

119901119894119862 =

119893119894119862

119873 119901119894

119862 = 1119871 minus 1

119894 = 0 (1)

wherei represents a specific intensity level ie 0 le 119894 le 119871 minus1 C represents the component of the image 119862 = 119877119866 119861 for

RGB imagesN represents the total number of pixels in the image and 119893119894

119862 denotes the number of pixels for the

corresponding intensity levels i in component C or 119893119894119862

represents an image histogram for each component C which can be normalized and regarded as the probability

distribution119901119894119862 The total mean of each component of the

image can be easily calculated as

120583119879119862 = 119894119901119894

119862 = 1119871 minus 1

119894 = 0 (2)

The probabilit ies of occurrence 119908119895119862 of classes 1198631

119862hellip 119863119899119862

are given by

119908119895119862 =

119901119894

119862 119905119895119862

119894 = 0 119895 = 1

119901119894119862

119905119895119862

119894 = 119905119895 minus 1119862 + 1

1 lt 119895 lt 119899

119901119894119862

119871 minus 1

119894 = 119905119895 minus 1119862 + 1

119895 = 119899

(3)

The mean of each class 120583119895119862 can then be calculated as

120583119895119862 =

119901119894119862

119908119895119862 119902

119905119895119862

119894 = 0 119895 = 1

119901119894119862

119908119895119862

119905119895119862

119894 = 119905119895 minus 1119862 + 1

1 lt 119895 lt 119899

119901119894119862

119908119895119862 119871 minus 1

119894 = 119905119895 minus 1119862 + 1

119895 = 119899

(4)

The simplest and computationally most efficient method of obtaining the optimal threshold is the one that maximizes the

between-class variance of each component which can be generally defined by

1205901198611198622

= 119908119895119862 120583119895

119862 minus 120583119879119862

2119899119895 = 1 (5)

wherei represents a specific class in such a way that 119908119895119862 and

120583119895119862 are the probability of occurrence and the mean of class j

respectivelyThe problem of n-level thresholding is reduced to

an optimization problem to search for the thresholds 119905119895119862 that

International Journal of Pure and Applied Mathematics Special Issue

137

maximize the objective functions (ie fitness function) of

each image component C generally given in equation 6 and the model results are displayed in Figure 2

120593119862 = max

1lt1199051119862 lt⋯lt119871minus1

1205901198611198622

119905119895119862 (6)

Fig 2 (a) Thermal images and (b) DPSO segmented images

B Active Contour Image Segmentation

Image segmentation is a central task in solving the region of

interest problem in image processing In general there are

three conventional methods of image segmentation procedures

like pixel based methods region based methods and edge

based methods all of which depends the local information of

the image [38] In our paper hybrid approach to image

segmentation is introduced named as Active contours without

edges [39][40] helps to find object boundary in a given image

based on curve evolution technique [41][42] popularly known

as level set method The basic impression of the level set

method or any active contour method is to evolve a curve over

time so that the curve moves towards its interiornormal and

when the stopping conditions are met the curve forms an

outline around theobject of interest For a g iven image 119868 [43]

we can create a level set function empty 119909 119910 withthe same size o f

the image 119868to describe the contour The contour is defined as

the zerolevel set of the function emptyas given in equation 7

119862 = 119909 119910 119891 119909 119910 = 0 (7)

(i) Energy Equation

The evolution of the initial contour is guided by an energy equation For the contour with an Signed Distance Function

(SDF) (empty119888 119909 119910 ) the energy function can be expressed as

119864 119862 = 119864 empty119888 119909 119910 = 1199081119864119868119898119886119892119890 119862 + 1199082119864119878119893119886119901119890 119862 +

1199083119864119877119890119892119906119897119886119903119894119911119886119905119894119900119899 119862 (8)

Where1199081 1199082and 1199083are real valued positive constant

weighting factors The image term119864119868119898119886119892119890 119862 attracts the

contour towards the object boundary 119864119878119893119886119901119890 119862 the shape

term penalizes the curve for deviating from uniformlayer

thickness [44] Lastly the regularizat ion

term119864119877119890119892119906119897119886119903119894119911119886119905119894119900119899 119862 helps to create a min imal length

smooth contour [45]Based on the combination of these energy

equation components (empty119888 119909 119910 ) is deformed to min imize

(empty119888 119909 119910 119905 )

(ii) Image term

119864119868119898119886119892119890 119862 =

1205821 119868 119909 119910 minus 1198881 2119889119909119889119910

119903119890119892119894119900119899 119887119890119905119908119890119890119899 119862119894 119886119899119889 119862119894minus1

+ 1205822 119868 119909 119910 minus 1198882 2

119903119890119892119894119900119899 119887119890119905119908119890119890119899 119862119894 119886119899119889 119862119894+1119889119909119889119910(9)

The image term divides the image into regions inside and

outside of the contour 119862 The values 1198621and 1198622are the values

of the mean pixel intensity inside and outside of the contour

respectively The constants 1205821and1205822are constants typically

both set to 1 This term reaches a minimum when the contour

divides the area inside and outside in regions of constant

homogeneity ie when lies along an object boundary [46]

Using the level set formulation the image term can be

expressed as

119864119868119898119886119892119890 = 1205821 119868 119909 119910 minus 1198881 2119867 empty119894 minus 1 119909 119910 1

minus 119867 empty119894 119909119910 119889119909119889119910

+ 1205822 119868 119909 119910 minus 1198882 2119867 empty119894 119909119910 1 minus 119867 empty119894+ 1 119909119910 119889119909119889119910

(10)

Where

119867 empty119894 minus 1 119909119910 1minus 119867 empty119894 119909119910 119886119899119889 119867 empty119894 119909 119910 1 minus

119867 empty119894+ 1 119909119910 are used to select the regions inside and

outside respectively

(iii) Shape term

The shape term is to say that each layer should be parallel to

the layer immediately above it Thus the shape term was

designed to penalize movement away from consistent

distances between boundaries For the boundary the boundary

is used for comparison The shape term is expressed by

119864119878119893119886119901119890 119862119894

= 119898119886119909 0 119862119894 119909 minus119862119894 minus 1 119909 minus 119880119894 119862119894 119909 minus 119862119894 minus 1 119909 minus119909119871119894 119889119909 (11)

Using the level set formulation the shape force term becomes

119864119868119898119886119892119890 empty119894 119909119910 = 119898119886119909 0 119910 minus119862119894 minus 1 119909 minus119880119894 119910 minus

119862119894 minus 1 119909 minus 119871119894 120575 empty119894 119909 119910 |nablaempty119894 119909 119910 |119889119909119889119910

(12)

Where120575 empty119894 119909 119910 |nablaempty119894 119909 119910 |is used to select the current

boundary region

(iv) Regularization term

International Journal of Pure and Applied Mathematics Special Issue

138

The last term in the regularizat ion is used to encourage

smooth short contours [47] The force term can be expressed

simply as

119864119877119890119892119906119897119886119903119894119911119886119905119894119900119899 empty119894 119909119910 = 120575 empty119894 119909119910 |nablaempty119894 119909119910 |119889119909119889119910 (13)

The results of the active contour image segmentation are

displayed in Figure 3 and histogram representations are given

in Figure 4

Fig 3 Top row DPSO segmented images Bottom row Active contour

segmented images

Fig 4 (a) Thermal image(b) Histogram representation of thermal image (c) DPSO segmented image (d) DPSO segmented histogram representation (e) Active contour segmented image (f) Histogram of Active contour image

C CORF edge detector

The implementation of the proposed CORF operator is rather

straightforward it includes blurring (achieved by convolving

with a Gaussian function) of halfwave rectified responses of

DoG operators shifting appropriately these blurred res ponses

by different vectors which are determined in the configuration

of the operator and using them for the pixel-wise evaluation

of a weighted geometric mean that gives the output of the

CORF operatorWe apply a classical two-step procedure in

computer vision thatwas proposed by [48] and [49] to obtain a

binary contour mapfrom the output of the concerned model

The first step consists ofedge thinning by non-maximum

suppression to determine theridges in the given response

image Then we apply hysteresis thresholding to obtain a

binary contour map The latter steprequires a high and a low

threshold value Similar to the work in[50] we set the low

threshold value to a fraction (05) of the highthreshold For a

given image we set the high threshold to be thelowest value

of the strongest f pixels in the thinned responseimage The

given value of the parameter f is a fraction of the totalnumber

of pixels in the image The resulting binary map containsthe

strongest fraction f of contour pixels together with

anyconnected ones that are achieved by hysteresis

thresholding The parameters used for the CORF operator are

the number of orientations nϴ (n=12 for ϴ=П6) a scale

parameter σ wavelength λ= σ4 and a spatial aspect ratio

γ=05

(i) Non-maximum suppression edge thinning

TheNon-maxima suppression thins the areas in which

119862120590 119909 119910 is non-zero to one-pixel wide candidate contours as

follows For each position 119909 119910 two responses Cσ(x|y

|) and

Cσ(x||y

||) in adjacent positions (x

|y

|) and (x

||y

||) that are

intersection points of a line passing through 119909 119910 in

orientation 120579120590 119909 119910 and a square defined by the diagonal

points of an 8-neighbourhood are computed by linear

interpolation as given by Figure 5 If the response

119862120590 119909 119910 at 119909 119910 is greater than both these values (ie it is a

local maximumalong the concerned line) it is retained

otherwise it isassigned the value zero

Fig 5 Interpolated responses at positions (x|y

|) and (x

||y

||) Non-

maximasuppression retains the value in the central pixel ethx yTHORN if it is larger

than thevalues at (x|y

|) and (x

||y

||)

Fig 6 (a) Image after active contour segmentation (b) One pixel binarized hysteresis threshold image (c) Image after CORF edge detection

International Journal of Pure and Applied Mathematics Special Issue

139

ii) Binarizat ion by Hysteresis thresholding

Next a binary map is computed from the candidate contour

pixels by hysteresis thresholding This process involves two

threshold values TLand TH TLltTH Commonly the high

threshold value THis computed as a (1-p)-quantile of the

distribution of the response values at the candidate contour

pixels where p is the minimum fraction of candidate pixels to

be retained in the contour map Candidate contour pixels with

responses higher than th are definitely retained in the contour

map while the ones with responses below the low threshold

TLare discarded Candidate contour pixels with responses

between TLand THare retained if they can be connected to any

candidate contour pixel with a response higher than THthrough

a chain of other candidate contour pixels with responses larger

than TL Figure 6 gives the results of edge thinning by non-

maximum suppression to one pixel and CORF edge detection

by hysteresis thresholding

D FSIM and SSIM

The aim of objective Image Quality Assessment (IQA) is to

develop mathemat ical models that are able to forecast the

quality of an image precisely and spontaneously An ideal

objective IQA method should be able to simulate the quality

predictions of an average human observer The proper IQA

method calculates the similarity index using a mathemat ical

model by quantizing the distortion image and the reference

image The main feature of the proper IQA is that it can be

embedded in real t ime image processing system The most

advanced method to perform IQA is Structure Similarity Index

Measurement (SSIM) [51] The various features like

luminance contrast and structure are compared in the SSIM

Almost all these features are consistent with the Human

Visual System (HVS) and are compatible But there are few

drawbacks as the luminance and contrast are sensitive to the

illumination To overcome the drawbacks of the

aforementioned technique Feature Similarity Index

Measurement (FSIM) has come into existence [52] In FSIM

two features main ly Phase Congruency (PC) [53] [54] and

Gradient Magnitude (GM) are considered To compute the PC

of 2D grayscale images The 1D log-Gabor filters described

earlier can be extended to 2D ones by simply applying some

spreading function across thefilter perpendicular to its

orientation One widely used spreading functionis Gaussian

[55] [56] and [57] By using Gaussian as the spreading

function the 2D log-Gabor function has the following transfer

function

1198662 120596120579119895 = 119890119909119901 119897119900119892 120596 1205960

2

21205901199032

119890119909119901 120579minus120579119895

2

21205901205792

(14)

Where 120579119895 = 119895120587 119869 119895 = 01hellip 119869 minus 1 the orientation angle of

the filter is 119869 is the number of orientations and 120590120579determines

the filter‟s angular bandwidthBy modulat ing 120596120579 and 120579119895 and

convolving 1198662with the 2D image we get a set of responses at

each point x as 119890119899120579119895 119883 119874119899 120579119895

119883 The local amplitude on

scale n and orientation 120579119895is119860119899120579119895 119883 = 119890119899 120579119895

119883 2 +119874119899 120579119895 119883 2

and the local energy along orientation 120579119895 is119864120579119895 119883 =

119865120579119895 119883 2 + 119867120579119895

119883 2 where119865120579119895 119883 = 119890119899 120579119895

119883 119899 and

119867120579119895 119883 = 119900119899 120579119895

119883 119899 The 2D PC at x is defined as

1198751198622119863 119883 = 119864120579 119895

119883 119895

휀+ 119860119899 120579 119895 119883 119895119899

(15)

It should be noted that 1198751198622119863 119883 is a real number within 0~1

(i) The FS IM index

The computation of FSIM index consists of two stages In the

first stage the local similarity map is computed and then in

the second stage we pool the similarity map into a single

similarity score We separate the feature similarity

measurement between 1198911 119883 and 1198912 119883 into two

components each for PC or GM First the similarity measure

for 1198751198621 119883 and 1198751198622 119883 is defined as

119878119875119862 119883 =21198751198621 119883 1198751198622 119883 +1198791

11987511986212 119883 +1198751198622

2 119883 +1198791 (16)

where 1198791 is a positive constant to increase the stability of SPC

(such a consideration was also included in SSIM [51]) In practice the determination of 1198791 depends on the dynamic

range of PC values Equation 16 is a commonly used measure

to define the similarity of two positive real numbers and its

result ranges within [0 1] Similarly the GM values 1198661 119883

and 1198662 119883 are compared and the similarity measure is defined

as

119878119866 119883 =21198661 119883 1198662 119883 +1198792

11986612 119883 +1198662

2 119883 +1198792 (17)

where 1198792 is a positive constant depending on the dynamic

range of GM values In our experiments both 1198791 and 1198792 will

be fixed to all databases so that the proposed FSIM can be conveniently used Then 119878119875119862 119883 and 119878119866 119883 are combined to

get the similarity 119878119871 119883 of 1198911 119883 and 1198912 119883 We define

119878119871 119883 as

119878119871 119883 = 119878119875119862 119883 120572

119878119866 119883 120573

(18)

where 120572 and 120573 are parameters used to adjust the relative

importance of PC and GM features In this paper we set 120572 = 120573 =1 for simplicity Thus119878119871 119883 = 119878119875119862 119883 119878119866 119883 Having

obtained the similarity 119878119871 119883 at each location 119883 the overall

similarity between 1198911and 1198912 can becalculated However

different locations have different contributions to HVS‟

perception of the image For example edge locations convey

more crucial v isual information than the locations within a

smooth area Since human visual cortex is sensitive to phase

congruent structures [54] the PC value at a location canreflect

how likely it is a perceptibly significant structure point Intuitively for a given location 119883 if anyone of 1198911 119883 and

1198912 119883 has a significant PC value it implies that this position x

International Journal of Pure and Applied Mathematics Special Issue

140

will have a high impact on HVS in evaluating the similarity between 1198911 and 1198912 Therefore we use 119875119862119898 119883 =

max(1198751198621 119883 1198751198622 119883 ) to weight the importance of 119878119871 119883 in

the overall similarity between 1198911 and 1198912 and accordingly the

FSIM index between 1198911and 1198912 is defined as

119865119878119868119872 = 119878119871 119883 119883 isinΩ 119875119862119898 119883

119875119862119898 119883 119883isinΩ (19)

where Ω means the whole image spatial domain

(ii) Structural similarity index (SSIM)

The SSIM algorithm performs similarity measurement in three

steps luminance comparison contrast comparison and

structure comparison First the luminance of each image

signal is compared The estimated mean intensity is computed

as follows

120583119903119890119891 =1

119882119867 119868119903119890119891 119894 119895

119882119894 = 1

119867119895 = 1 (20)

The luminance comparison function 119897 119868119903119890119891 119868119905119904119905 is a

function of 120583119903119890119891 and 120583119905119904119905Second the contrast of each image

signal is compared For estimat ing the contrast standard

deviation is being used An unbiased estimate of standard

deviation in discrete form is as follows 120590119903119890119891

= 1

119882119867minus1 119868119903119890119891 119894 119895 minus 120583119903119890119891

2119882119894 = 1

119867119895 = 1

1

2

(21)

The contrast comparison function 119888 119868119903119890119891 119868119905119904119905 is a function

of120590119903119890119891 and 120590119905119904119905 Third the structure of each image signal is

compared Structure comparison function119904 119868119903119890119891 119868119905119904119905 is a

function of 119868119903119890119891 minus 120583119903119890119891 120590119903119890119891 and

119868119905119904119905 minus 120583119905119904119905 120590119905119904119905 Finally three comparison functions are

combined and an overall similarity measure is produced The

overall similarity measure119878 119868119903119890119891 119868119905119904119905 is a function of

119897 119868119903119890119891 119868119905119904119905 119888 119868119903119890119891 119868119905119904119905 119888 119868119903119890119891 119868119905119904119905 and 119904 119868119903119890119891 119868119905119904119905

Definitions of119897 119868119903119890119891 119868119905119904119905 119888 119868119903119890119891 119868119905119904119905 and119904 119868119903119890119891 119868119905119904119905 are as

follows

For luminance comparison function we have

119904 119868119903119890119891 119868119905119904119905 =2120583119903119890119891 120583119905119904119905 +1198791

1205831199031198901198912 +120583119905119904119905

2 +1198791 (21)

where 1198791 is a positive stabilizing constant chosen to prevent

the denominator from becoming too small We have

1198791 = 1199051119863 2 (22)

where D is the dynamic range of pixel values and 1199051 ltlt 1 is

a small constant For contrast comparison function we have

119888 119868119903119890119891 119868119905119904119905 =2120590119903119890119891 120590119905119904119905 +1198792

1205901199031198901198912 +120590119905119904119905

2 +1198792 (23)

where 1198792 = 1199052119863 2is a positive stabilizing constant

And1199052 ltlt 1 For structure comparison function we have

119904 119868119903119890119891 119868119905119904119905 =120590119903119890119891 119905119904119905+1198793

120590119903119890119891 120590119905119904119905 +1198793 (24)

where 1198793 is a positive stabilizing constant In (58)120590119903119890119891 119905119904119905 is

the correlation coefficient between the reference and test images In the discrete form120590119903119890119891 119905119904119905 can be estimated by

120590119903119890119891 119905119904119905 =1

119882119867minus1 119868119903119890119891 119894 119895 minus 120583119903119890119891 119868119905119904119905 119894 119895 minus

119882119894 = 1

119867119895 = 1

120583119905119904119905 (25)

Finally structural similarity index is defined as

119878119878119868119872 119868119903119890119891 119868119905119904119905 =

119897 119868119903119890119891 119868119905119904119905 120572 119888 119868119903119890119891 119868119905119904119905

120573 119904 119868119903119890119891 119868119905119904119905

120574 (26)

where 120572 120573 and 120574The universal quality index (UQI) [5960] is a special case of the SSIM index when1198791 = 1198792 = 1198793 = 0

and 120572 = 120573 = 120574 = 1 Since image statistical features and

distortions are usually space-variant authors of [60] employ

the SSIM index locally instead of globally Another reason for

this is that by applying the SSIM index locally a quality map

of the image which conveys more information about the

quality degradation can be generated

TABLE I SAMPLE TEN SUBJECT‟S FSIM VALUES WITH RESPECT TO EACH OTHER

Subject No

11 12 13 14 15 16 17 18 19 20

11 9342 7906 7438 7442 7648 7566 7509 78 7441 7597

12 7906 9523 734 7135 7459 745 7394 7505 7335 7449

13 7438 734 9705 743 7943 7264 776 7417 7941 7735

14 7442 7135 743 9429 8081 7252 7428 7478 7604 7406

15 7648 7459 7943 8081 943 7734 818 7903 834 8126

16 7566 745 7264 7252 7734 9247 7599 8769 7523 7713

17 7509 7394 776 7428 8189 7599 934 7552 8102 8612

18 7801 7505 7417 7478 7903 8769 7552 9342 7631 7669

19 7441 7335 7941 7604 834 7523 8102 7631 9693 806

20 7597 7449 7735 7464 8126 7713 8612 7669 806 9479

International Journal of Pure and Applied Mathematics Special Issue

141

TABLE II SAMPLE TEN SUBJECT‟S SSIM VALUES WITH RESPECT TO EACH OTHER

Subject No

11 12 13 14 15 16 17 18 19 20

11 9044 7333 6507 6937 7054 7217 6717 7433 6588 6854

12 7333 9327 6249 6298 6574 6905 6357 6976 6258 6421

13 6507 6249 9643 6744 7311 6586 7173 671 7242 7014

14 6937 6298 6744 9155 7673 6857 6911 7007 7009 6874

15 7054 6574 7311 7673 9158 7325 7676 7475 7685 7621

16 7217 6905 6586 6857 7325 925 711 867 694 7189

17 6717 6357 7173 6911 7676 711 9147 7083 7443 822

18 7433 6976 671 7007 7475 867 7083 9236 7054 7145

19 6588 6258 7242 7009 7685 694 7443 7054 9495 7423

20 6854 6421 7014 6874 7621 7189 822 7145 7423 9251

IV EXPERIMENTAL RESULTS AND ANALYSIS

In this section the performance of IQA techniques like FSIM

and SSIM are evaluated The parameters required in the

proposed methods were set as n = 4 J = 4 σr = 05978 σθ =

06545 T1 = 085 T2 = 160 T3 = T4 = 200 and λ = 003

Besides the center frequencies of the log-Gabor filters at four

scales were set as 16 112 124 and 148 These parameters

were then fixed for all the following experiments conducted

We take twenty set of database in which each database

consists of around seventy images Each and every image is

taken as the reference image and measured the similarity with

all other images present and the results are tabulated for FSIM

in Table I whereas for SSIM the results are tabulated in Table

II The average similarity index for each and every database

for the FSIM and SSIM are given in Figure 7 The results

clearly indicate that similarity measure is a good sign of a

quality measure as well as good metric to identify the

similarity between the images The results also gave a clear

indication that FSIM overcomes the drawbacks of SSIM and

gave a good measurement when compared to the SSIM

Fig 7 Graphical representation of FSIM and SSIM average values of the

given database

V CONCLUSION AND FUTURE WORK

The proposed work implemented the similarity index

assessment of thermal images following the sequence of the

work g iven as follows Darwinian Particle Swarm

Optimization is used for image segmentation as a multi-

threshold technique which has overcome various drawbacks

like computational time feature selectivity stability and

feasibility DPSO is better when compared to other

conventional multi-threshold techniques like Otsu image

segmentation fuzzy clustering PSO and ant colony

optimization Active contour image segmentation was

performed which is based on the level set based segmentation

method of Mumford Shah model producing binary image The

CORF operator extracts the contour image using Difference of

Gaussians and hysteresis thresholding The similarities of the

results are compared using FSIM and SSIM FSIM

outperforms the results of SSIM The results are good enough

to show that Image Quality Assessment techniques are helpful

in the process of identificat ion and classification of subjects

The given below points can be considered as a future work (i)

The results can be compared with other IQA metrics and (ii)

The proposed approach need to be explored in the domain of

medical imaging and satellite communicat ion

REFERENCES

[1] W Zhao R Chellappa A Rosenfeld and P Phillips ldquoFace recognition

A literature surveyrdquo ACM Computer Survey vol 35 no 4 pp 399-458 December 2003

[2] T Bourlai A Ross C Chen and L Hornak A study on using mid-wave infrared imagesfor face recognition In Proc SPIE 2012

[3] R S Ghiass O Arandjelovic A Bendada and X Maldague Infrared face recognition a literature review In Proc International Joint Conference on Neural Networks pages2791-2800 2013

[4] Yufeng Zheng ldquoFace detection and eyeglasses detection for thermal face recognitionrdquo ISampTSPIE Electronic Imaging Conference 22-26 January 2012 in Burlingame California United States

[5] F J Prokoski R B Riedel and J S Coffin ldquoIdentification of individuals by means of facial thermographyrdquo in Proceedings of The IEEE 1992 International Carnahan Conference on Security Technology Crime Countermeasures Atlanta GA USA 14-16 Oct pp 120-125 IEEE 1992

[6] Cutler R ldquoFace recognition using infrared images and eigenfacesrdquo httpciteseeristpsueducutler96facehtml April 1996 visited July 2007

[7] Socolinsky D Selinger A ldquoA comparative analysis of face recognition performance with visible and thermal infrared imageryrdquo Proceedings of the International Conference o Pattern Recognition (ICPR02) vol2 p 40217 Quebec Canada August 2002

[8] Socolinsky D Selinger A Neuheisel J ldquoFace recognition with visible and thermal infrared imageryrdquo Computer Vision amp Image Understanding vol 91 p 72-114 2003

50

60

70

80

90

100

1 3 5 7 9 11 13 15 17 19

FS

IM a

nd

SS

IM V

alu

es

Subject No

FSIM

SSIM

International Journal of Pure and Applied Mathematics Special Issue

142

[9] H-W Tzeng H-C Lee and M-Y Chen The design of isotherm face recognition technique based on nostril localization In Proc International Conference on System Science and Engineering pages 82-86 2011

[10] O Arandjelovic R I Hammoud and R Cipolla Thermal and re ectance based personal identification methodology in challenging variable illuminations Pattern Recognition 43(5)1801-1813 2010

[11] T Jin C Shouming X Xiuzhen and J Gu Eyes localization in an infrared image In Proc IEEE International Conference on Automation and Logistics (ICAL) pages 217-222 2009

[12] T Bourlai and Z Jafri Eye detection in the middle-wave infrared spectrum Towards recognition in the dark In Proc IEEE International Workshop on Information Forensic and Security (WIFS) pages 1-6 2011

[13] B Martinez X Binefa and M Pantic Facial component detection in thermal imagery In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 48-54 2010

[14] Chen X Jing Z Xiao G ldquoFuzzy fusion for face recognitionrdquo Proceedings of the International Conference on Fuzzy Systems and Knowledge Discovery (FSKD05) p 672- 675 Changsha China August 2005

[15] S Zhao and R Grigat An automatic face recognition system in the near infrared spectrum MLDM pages 437-444 2005

[16] T Elguebaly and N Bouguila ldquoA Bayesian method for infrared face recognitionrdquo Machine Vision Beyond Visible Spectrum 2011

[17] Y Yoshitomi T Miyaura S Tomita and S Kimura Face identification using thermalimage processing RO-MAN pages 374-379 1997

[18] S Li R Chu M Ao L Zhang and R He Highly accurate and fast face recognitionusing near infrared images In Proc IAPR International Conference on Biometricspages 151-158 2006

[19] H Maeng H-C Choi U Park S-W Lee and A K Jain NFRAD Near-infraredface recognition at a distance In Proc International Joint Conference on Biometrics(IJCB) pages 1-7 2011

[20] D Goswami C H Chan D Windridge and J Kittler Evaluation of face recognition system in heterogeneous environments (visible vs NIR) In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 2160-2167 2011

[21] A Srivastana and X Liu Statistical hypothesis pruning for recognizing faces from infrared images Image and Vision Computing 21(7)651-661 2003

[22] Z Xie SWu G Liu and Z Fang Infrared face recognition based on radiant energy and curvelet transformation In Proc International Conference on Information Assurance and Security (IAS) 2215-218 2009

[23] P Buddharaju I Pavlidis and P Tsiamyrtzis Pose-invariant physiological face recognition in the thermal infrared spectrum In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 53-60 2006

[24] P Buddharaju and I Pavlidis Physiological face recognition is coming of age In Proc IEEE Conference on Computer Vision and Pattern Recognition pages 128-135 2009

[25] T R Gault N Blumenthal A A Farag and T Starr Extraction of the superficial facial vasculature vital signs waveforms and rates using thermal imaging In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 1-8 2010

[26] A Seal M Nasipuri D Bhattacharjee and DK Basu Minutiae based thermal face recognition using blood perfusion data International Conference on Image Information Processing pages 1-4 2011

[27] S Cho L Wang and W J Ong Thermal imprint feature analysis for face recognitionISIE pages 1875-1880 2009

[28] R S Ghiass O Arandjelovic A Bendada and X Maldague Vesselness features and the inverse compositional AAM for robust face recognition using thermal IR In Proc AAAI Conference on Artificial Intelligence pages 357-364 2013

[29] S Wu Z Gu K A Chia and S H Ong Infrared facial recognition using modified blood perfusion ICICS pages 1-5 2007

[30] Z Xie S Wu G Liu and Z Fang Infrared face recognition method based on blood perfusion image and curvelet transformation In Proc

International Conference on Wavelet Analysis and Pattern Recognition pages 360-364 2009

[31] Kennedy J amp Eberhart R ldquoA new optimizer using particle swarm theoryrdquo in Proceedings of the IEEE sixth international symposium on micro machine andhuman science pp 39ndash43 1995

[32] Tillett J Rao T M Sahin F Rao R amp Brockport S (2005) Darwinian Particle Swarm Optimization In Proceedings of the 2nd Indian international conference onartificial intelligence (pp 1474ndash1487)

[33] Z Chenglin S Xuebin S Songlin and J Ting ldquoFault diagnosis of sensor by chaos particle swarm optimization algorithm and support vector machinerdquo Expert Systems with Applications vol 38 no 8 pp 9908ndash9912 2011

[34] P Ghamisi M S Couceiro J A Benediktsson and N M F Ferreira An Efficient Method for Segmentation of Images Based on Fractional Calculus and Natural Selection Expert Systems With Applications vol 39 no 16 pp 12407- 2417 Nov 2012

[35] P Ghamisi M S Couceiro F M L Martins and J A Benediktsson Multi-level Image Segmentation Based on Fractional-Order Darwinian Particle Swarm Optimization IEEE Transactions on Geoscience and Remote Sensing vol 52 no 5 pp 2382-2394 May 2014

[36] M S Couceiro N M F Ferreira and J A T Machado ldquoFractional order Darwinian particle swarm optimizationrdquo in proc Symp FSS Coimbra Portugal pp 4-5 Nov 2011

[37] P Ghamisi M S Couceiro and J A Benediktsson Classification of Hyperspectral Images with Binary Fractional Order Darwinian PSO and Random Forests in Proc SPIE Image and Signal Processing for Remote Sensing XIX 2013

[38] G Majumder and M K Bhowmik ldquoGabor-Fast ICA feature extraction for thermal face recognition using linear kernel support vector machinerdquo Computational Intelligence and Networks (CINE) 2015 International Conference on DOI 101109CINE201514 pp21 ndash 25 2015

[39] T Chan L Vese and Y Sandberg Active contours without edges for vector-valued images Journal of Visual Communications and Image Representation 11 no 2 (2000) pp 130-141

[40] D Mumford and J Shah Optimal approximation by piecewise smooth functions and associated variational problems Comm Pure Appl Math 42 1989 pp 577-685

[41] M Sussman P Smereka and S Osher A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow J Comput Phys V 119 (1994) pp 146-159

[42] L Vese and T Chan A multiphase level set framework for image segmentation using the mumford and shah model International Journal of Computer Vision vol 50 pp 271-293 2002

[43] T F Chan and L A Vese Image segmentation using level sets and the piecewise-constant Mumford-Shah model 2000

[44] D Cremers F R Schmidt and F Barthel Shape priors in variational image segmentation Convexity lipschitz continuity and globally optimal solutions in Computer Vision and Pattern Recognition 2008 CVPR 2008 IEEE Conference on 2008 pp 1-6

[45] S Osher and J A Sethian Fronts propagating with curvature-dependent speed algorithms based on Hamilton-Jacobi formulations Journal of computat ional physics vol 79 pp 12-49 1988

[46] R Ronfard Region-based strategies for active contour models International Journal of Computer Vision vol 13 pp 229-251 1994

[47] K Siddiqi Y B Lauziere A Tannenbaum and S W Zucker Area and length minimizing flows for shape segmentation Image Processing IEEE Transactions on vol 7 pp 433-443 1998

[48] Cosmin Grigorescu Nicolai Petkov Michel A Westenberg Contour and boundary detection improved by surround suppression of texture edges Image and Vision Computing Vol 22 pp 609-622 2004

[49] Azzopardi G Petkov N A CORF computational model of a simple cell that relies on LGN input outperforms the Gabor function model Biol Cybern 106(3) 177ndash189 (2012)

[50] Azzopardi G Petkov N Contour detection by CORF operator In Villa AEP Duch W Erdi P Masulli F Palm G (eds) ICANN 2012 Part I LNCS vol acute 7552 pp 395ndash402 Springer Heidelberg (2012)

International Journal of Pure and Applied Mathematics Special Issue

143

[51] Z Wang AC Bovik HR Sheikh and EP Simoncelli ldquoImage quality assessment from error visibility to structural similarityrdquo IEEE Trans Image Process vol 13 no 4 pp 600-612 Apr 2004

[52] Lin Zhang Lei Zhang Xuanqin Mou and David Zhang FSIM a feature similarity index for image quality assessment IEEE Transactions on Image Processing vol 20 no 8 pp 2378-2386 2011

[53] P Kovesi ldquoImage features from phase congruencyrdquo Videre J Comp Vis Res vol 1 no 3 pp 1-26 1999

[54] L Henriksson A Hyvaumlrinen and S Vanni ldquoRepresentation of cross-frequency spatial phase relationships in human visual cortexrdquo J Neuroscience vol 29 no 45 pp 14342-14351 Nov 2009

[55] C Mancas-Thillou and B Gosselin ldquoCharacter segmentation-by-recognition using log-Gabor filtersrdquo in Proc Int Conf Pattern Recognit 2006 pp 901-904

[56] S Fischer F Šroubek L Perrinet R Redondo and G Cristoacutebal ldquoSelf-invertible 2D log-Gabor waveletsrdquo Int J Computer Vision vol 75 no 2 pp 231-246 Nov 2007

[57] W Wang J Li F Huang and H Feng ldquoDesign and implementation of log-Gabor filter in fingerprint image enhancementrdquo Pattern Recognit Letters vol 29 no 3 pp 301-308 Feb 2008

[58] H R Sheikh and A C Bovik Image information and visual quality IEEE Trans Image Processing vol 15 pp 430-444 Feb 2006

[59] Z Wang Rate scalable foveated image and video communications PhD thesis Dept of ECE the University of Texas at Austin Dec 2001

[60] Z Wang and A C Bovik A universal image quality index IEEE Signal Processing Letters vol 9 pp 81-84 March 2002

International Journal of Pure and Applied Mathematics Special Issue

144

145

146

maximize the objective functions (ie fitness function) of

each image component C generally given in equation 6 and the model results are displayed in Figure 2

120593119862 = max

1lt1199051119862 lt⋯lt119871minus1

1205901198611198622

119905119895119862 (6)

Fig 2 (a) Thermal images and (b) DPSO segmented images

B Active Contour Image Segmentation

Image segmentation is a central task in solving the region of

interest problem in image processing In general there are

three conventional methods of image segmentation procedures

like pixel based methods region based methods and edge

based methods all of which depends the local information of

the image [38] In our paper hybrid approach to image

segmentation is introduced named as Active contours without

edges [39][40] helps to find object boundary in a given image

based on curve evolution technique [41][42] popularly known

as level set method The basic impression of the level set

method or any active contour method is to evolve a curve over

time so that the curve moves towards its interiornormal and

when the stopping conditions are met the curve forms an

outline around theobject of interest For a g iven image 119868 [43]

we can create a level set function empty 119909 119910 withthe same size o f

the image 119868to describe the contour The contour is defined as

the zerolevel set of the function emptyas given in equation 7

119862 = 119909 119910 119891 119909 119910 = 0 (7)

(i) Energy Equation

The evolution of the initial contour is guided by an energy equation For the contour with an Signed Distance Function

(SDF) (empty119888 119909 119910 ) the energy function can be expressed as

119864 119862 = 119864 empty119888 119909 119910 = 1199081119864119868119898119886119892119890 119862 + 1199082119864119878119893119886119901119890 119862 +

1199083119864119877119890119892119906119897119886119903119894119911119886119905119894119900119899 119862 (8)

Where1199081 1199082and 1199083are real valued positive constant

weighting factors The image term119864119868119898119886119892119890 119862 attracts the

contour towards the object boundary 119864119878119893119886119901119890 119862 the shape

term penalizes the curve for deviating from uniformlayer

thickness [44] Lastly the regularizat ion

term119864119877119890119892119906119897119886119903119894119911119886119905119894119900119899 119862 helps to create a min imal length

smooth contour [45]Based on the combination of these energy

equation components (empty119888 119909 119910 ) is deformed to min imize

(empty119888 119909 119910 119905 )

(ii) Image term

119864119868119898119886119892119890 119862 =

1205821 119868 119909 119910 minus 1198881 2119889119909119889119910

119903119890119892119894119900119899 119887119890119905119908119890119890119899 119862119894 119886119899119889 119862119894minus1

+ 1205822 119868 119909 119910 minus 1198882 2

119903119890119892119894119900119899 119887119890119905119908119890119890119899 119862119894 119886119899119889 119862119894+1119889119909119889119910(9)

The image term divides the image into regions inside and

outside of the contour 119862 The values 1198621and 1198622are the values

of the mean pixel intensity inside and outside of the contour

respectively The constants 1205821and1205822are constants typically

both set to 1 This term reaches a minimum when the contour

divides the area inside and outside in regions of constant

homogeneity ie when lies along an object boundary [46]

Using the level set formulation the image term can be

expressed as

119864119868119898119886119892119890 = 1205821 119868 119909 119910 minus 1198881 2119867 empty119894 minus 1 119909 119910 1

minus 119867 empty119894 119909119910 119889119909119889119910

+ 1205822 119868 119909 119910 minus 1198882 2119867 empty119894 119909119910 1 minus 119867 empty119894+ 1 119909119910 119889119909119889119910

(10)

Where

119867 empty119894 minus 1 119909119910 1minus 119867 empty119894 119909119910 119886119899119889 119867 empty119894 119909 119910 1 minus

119867 empty119894+ 1 119909119910 are used to select the regions inside and

outside respectively

(iii) Shape term

The shape term is to say that each layer should be parallel to

the layer immediately above it Thus the shape term was

designed to penalize movement away from consistent

distances between boundaries For the boundary the boundary

is used for comparison The shape term is expressed by

119864119878119893119886119901119890 119862119894

= 119898119886119909 0 119862119894 119909 minus119862119894 minus 1 119909 minus 119880119894 119862119894 119909 minus 119862119894 minus 1 119909 minus119909119871119894 119889119909 (11)

Using the level set formulation the shape force term becomes

119864119868119898119886119892119890 empty119894 119909119910 = 119898119886119909 0 119910 minus119862119894 minus 1 119909 minus119880119894 119910 minus

119862119894 minus 1 119909 minus 119871119894 120575 empty119894 119909 119910 |nablaempty119894 119909 119910 |119889119909119889119910

(12)

Where120575 empty119894 119909 119910 |nablaempty119894 119909 119910 |is used to select the current

boundary region

(iv) Regularization term

International Journal of Pure and Applied Mathematics Special Issue

138

The last term in the regularizat ion is used to encourage

smooth short contours [47] The force term can be expressed

simply as

119864119877119890119892119906119897119886119903119894119911119886119905119894119900119899 empty119894 119909119910 = 120575 empty119894 119909119910 |nablaempty119894 119909119910 |119889119909119889119910 (13)

The results of the active contour image segmentation are

displayed in Figure 3 and histogram representations are given

in Figure 4

Fig 3 Top row DPSO segmented images Bottom row Active contour

segmented images

Fig 4 (a) Thermal image(b) Histogram representation of thermal image (c) DPSO segmented image (d) DPSO segmented histogram representation (e) Active contour segmented image (f) Histogram of Active contour image

C CORF edge detector

The implementation of the proposed CORF operator is rather

straightforward it includes blurring (achieved by convolving

with a Gaussian function) of halfwave rectified responses of

DoG operators shifting appropriately these blurred res ponses

by different vectors which are determined in the configuration

of the operator and using them for the pixel-wise evaluation

of a weighted geometric mean that gives the output of the

CORF operatorWe apply a classical two-step procedure in

computer vision thatwas proposed by [48] and [49] to obtain a

binary contour mapfrom the output of the concerned model

The first step consists ofedge thinning by non-maximum

suppression to determine theridges in the given response

image Then we apply hysteresis thresholding to obtain a

binary contour map The latter steprequires a high and a low

threshold value Similar to the work in[50] we set the low

threshold value to a fraction (05) of the highthreshold For a

given image we set the high threshold to be thelowest value

of the strongest f pixels in the thinned responseimage The

given value of the parameter f is a fraction of the totalnumber

of pixels in the image The resulting binary map containsthe

strongest fraction f of contour pixels together with

anyconnected ones that are achieved by hysteresis

thresholding The parameters used for the CORF operator are

the number of orientations nϴ (n=12 for ϴ=П6) a scale

parameter σ wavelength λ= σ4 and a spatial aspect ratio

γ=05

(i) Non-maximum suppression edge thinning

TheNon-maxima suppression thins the areas in which

119862120590 119909 119910 is non-zero to one-pixel wide candidate contours as

follows For each position 119909 119910 two responses Cσ(x|y

|) and

Cσ(x||y

||) in adjacent positions (x

|y

|) and (x

||y

||) that are

intersection points of a line passing through 119909 119910 in

orientation 120579120590 119909 119910 and a square defined by the diagonal

points of an 8-neighbourhood are computed by linear

interpolation as given by Figure 5 If the response

119862120590 119909 119910 at 119909 119910 is greater than both these values (ie it is a

local maximumalong the concerned line) it is retained

otherwise it isassigned the value zero

Fig 5 Interpolated responses at positions (x|y

|) and (x

||y

||) Non-

maximasuppression retains the value in the central pixel ethx yTHORN if it is larger

than thevalues at (x|y

|) and (x

||y

||)

Fig 6 (a) Image after active contour segmentation (b) One pixel binarized hysteresis threshold image (c) Image after CORF edge detection

International Journal of Pure and Applied Mathematics Special Issue

139

ii) Binarizat ion by Hysteresis thresholding

Next a binary map is computed from the candidate contour

pixels by hysteresis thresholding This process involves two

threshold values TLand TH TLltTH Commonly the high

threshold value THis computed as a (1-p)-quantile of the

distribution of the response values at the candidate contour

pixels where p is the minimum fraction of candidate pixels to

be retained in the contour map Candidate contour pixels with

responses higher than th are definitely retained in the contour

map while the ones with responses below the low threshold

TLare discarded Candidate contour pixels with responses

between TLand THare retained if they can be connected to any

candidate contour pixel with a response higher than THthrough

a chain of other candidate contour pixels with responses larger

than TL Figure 6 gives the results of edge thinning by non-

maximum suppression to one pixel and CORF edge detection

by hysteresis thresholding

D FSIM and SSIM

The aim of objective Image Quality Assessment (IQA) is to

develop mathemat ical models that are able to forecast the

quality of an image precisely and spontaneously An ideal

objective IQA method should be able to simulate the quality

predictions of an average human observer The proper IQA

method calculates the similarity index using a mathemat ical

model by quantizing the distortion image and the reference

image The main feature of the proper IQA is that it can be

embedded in real t ime image processing system The most

advanced method to perform IQA is Structure Similarity Index

Measurement (SSIM) [51] The various features like

luminance contrast and structure are compared in the SSIM

Almost all these features are consistent with the Human

Visual System (HVS) and are compatible But there are few

drawbacks as the luminance and contrast are sensitive to the

illumination To overcome the drawbacks of the

aforementioned technique Feature Similarity Index

Measurement (FSIM) has come into existence [52] In FSIM

two features main ly Phase Congruency (PC) [53] [54] and

Gradient Magnitude (GM) are considered To compute the PC

of 2D grayscale images The 1D log-Gabor filters described

earlier can be extended to 2D ones by simply applying some

spreading function across thefilter perpendicular to its

orientation One widely used spreading functionis Gaussian

[55] [56] and [57] By using Gaussian as the spreading

function the 2D log-Gabor function has the following transfer

function

1198662 120596120579119895 = 119890119909119901 119897119900119892 120596 1205960

2

21205901199032

119890119909119901 120579minus120579119895

2

21205901205792

(14)

Where 120579119895 = 119895120587 119869 119895 = 01hellip 119869 minus 1 the orientation angle of

the filter is 119869 is the number of orientations and 120590120579determines

the filter‟s angular bandwidthBy modulat ing 120596120579 and 120579119895 and

convolving 1198662with the 2D image we get a set of responses at

each point x as 119890119899120579119895 119883 119874119899 120579119895

119883 The local amplitude on

scale n and orientation 120579119895is119860119899120579119895 119883 = 119890119899 120579119895

119883 2 +119874119899 120579119895 119883 2

and the local energy along orientation 120579119895 is119864120579119895 119883 =

119865120579119895 119883 2 + 119867120579119895

119883 2 where119865120579119895 119883 = 119890119899 120579119895

119883 119899 and

119867120579119895 119883 = 119900119899 120579119895

119883 119899 The 2D PC at x is defined as

1198751198622119863 119883 = 119864120579 119895

119883 119895

휀+ 119860119899 120579 119895 119883 119895119899

(15)

It should be noted that 1198751198622119863 119883 is a real number within 0~1

(i) The FS IM index

The computation of FSIM index consists of two stages In the

first stage the local similarity map is computed and then in

the second stage we pool the similarity map into a single

similarity score We separate the feature similarity

measurement between 1198911 119883 and 1198912 119883 into two

components each for PC or GM First the similarity measure

for 1198751198621 119883 and 1198751198622 119883 is defined as

119878119875119862 119883 =21198751198621 119883 1198751198622 119883 +1198791

11987511986212 119883 +1198751198622

2 119883 +1198791 (16)

where 1198791 is a positive constant to increase the stability of SPC

(such a consideration was also included in SSIM [51]) In practice the determination of 1198791 depends on the dynamic

range of PC values Equation 16 is a commonly used measure

to define the similarity of two positive real numbers and its

result ranges within [0 1] Similarly the GM values 1198661 119883

and 1198662 119883 are compared and the similarity measure is defined

as

119878119866 119883 =21198661 119883 1198662 119883 +1198792

11986612 119883 +1198662

2 119883 +1198792 (17)

where 1198792 is a positive constant depending on the dynamic

range of GM values In our experiments both 1198791 and 1198792 will

be fixed to all databases so that the proposed FSIM can be conveniently used Then 119878119875119862 119883 and 119878119866 119883 are combined to

get the similarity 119878119871 119883 of 1198911 119883 and 1198912 119883 We define

119878119871 119883 as

119878119871 119883 = 119878119875119862 119883 120572

119878119866 119883 120573

(18)

where 120572 and 120573 are parameters used to adjust the relative

importance of PC and GM features In this paper we set 120572 = 120573 =1 for simplicity Thus119878119871 119883 = 119878119875119862 119883 119878119866 119883 Having

obtained the similarity 119878119871 119883 at each location 119883 the overall

similarity between 1198911and 1198912 can becalculated However

different locations have different contributions to HVS‟

perception of the image For example edge locations convey

more crucial v isual information than the locations within a

smooth area Since human visual cortex is sensitive to phase

congruent structures [54] the PC value at a location canreflect

how likely it is a perceptibly significant structure point Intuitively for a given location 119883 if anyone of 1198911 119883 and

1198912 119883 has a significant PC value it implies that this position x

International Journal of Pure and Applied Mathematics Special Issue

140

will have a high impact on HVS in evaluating the similarity between 1198911 and 1198912 Therefore we use 119875119862119898 119883 =

max(1198751198621 119883 1198751198622 119883 ) to weight the importance of 119878119871 119883 in

the overall similarity between 1198911 and 1198912 and accordingly the

FSIM index between 1198911and 1198912 is defined as

119865119878119868119872 = 119878119871 119883 119883 isinΩ 119875119862119898 119883

119875119862119898 119883 119883isinΩ (19)

where Ω means the whole image spatial domain

(ii) Structural similarity index (SSIM)

The SSIM algorithm performs similarity measurement in three

steps luminance comparison contrast comparison and

structure comparison First the luminance of each image

signal is compared The estimated mean intensity is computed

as follows

120583119903119890119891 =1

119882119867 119868119903119890119891 119894 119895

119882119894 = 1

119867119895 = 1 (20)

The luminance comparison function 119897 119868119903119890119891 119868119905119904119905 is a

function of 120583119903119890119891 and 120583119905119904119905Second the contrast of each image

signal is compared For estimat ing the contrast standard

deviation is being used An unbiased estimate of standard

deviation in discrete form is as follows 120590119903119890119891

= 1

119882119867minus1 119868119903119890119891 119894 119895 minus 120583119903119890119891

2119882119894 = 1

119867119895 = 1

1

2

(21)

The contrast comparison function 119888 119868119903119890119891 119868119905119904119905 is a function

of120590119903119890119891 and 120590119905119904119905 Third the structure of each image signal is

compared Structure comparison function119904 119868119903119890119891 119868119905119904119905 is a

function of 119868119903119890119891 minus 120583119903119890119891 120590119903119890119891 and

119868119905119904119905 minus 120583119905119904119905 120590119905119904119905 Finally three comparison functions are

combined and an overall similarity measure is produced The

overall similarity measure119878 119868119903119890119891 119868119905119904119905 is a function of

119897 119868119903119890119891 119868119905119904119905 119888 119868119903119890119891 119868119905119904119905 119888 119868119903119890119891 119868119905119904119905 and 119904 119868119903119890119891 119868119905119904119905

Definitions of119897 119868119903119890119891 119868119905119904119905 119888 119868119903119890119891 119868119905119904119905 and119904 119868119903119890119891 119868119905119904119905 are as

follows

For luminance comparison function we have

119904 119868119903119890119891 119868119905119904119905 =2120583119903119890119891 120583119905119904119905 +1198791

1205831199031198901198912 +120583119905119904119905

2 +1198791 (21)

where 1198791 is a positive stabilizing constant chosen to prevent

the denominator from becoming too small We have

1198791 = 1199051119863 2 (22)

where D is the dynamic range of pixel values and 1199051 ltlt 1 is

a small constant For contrast comparison function we have

119888 119868119903119890119891 119868119905119904119905 =2120590119903119890119891 120590119905119904119905 +1198792

1205901199031198901198912 +120590119905119904119905

2 +1198792 (23)

where 1198792 = 1199052119863 2is a positive stabilizing constant

And1199052 ltlt 1 For structure comparison function we have

119904 119868119903119890119891 119868119905119904119905 =120590119903119890119891 119905119904119905+1198793

120590119903119890119891 120590119905119904119905 +1198793 (24)

where 1198793 is a positive stabilizing constant In (58)120590119903119890119891 119905119904119905 is

the correlation coefficient between the reference and test images In the discrete form120590119903119890119891 119905119904119905 can be estimated by

120590119903119890119891 119905119904119905 =1

119882119867minus1 119868119903119890119891 119894 119895 minus 120583119903119890119891 119868119905119904119905 119894 119895 minus

119882119894 = 1

119867119895 = 1

120583119905119904119905 (25)

Finally structural similarity index is defined as

119878119878119868119872 119868119903119890119891 119868119905119904119905 =

119897 119868119903119890119891 119868119905119904119905 120572 119888 119868119903119890119891 119868119905119904119905

120573 119904 119868119903119890119891 119868119905119904119905

120574 (26)

where 120572 120573 and 120574The universal quality index (UQI) [5960] is a special case of the SSIM index when1198791 = 1198792 = 1198793 = 0

and 120572 = 120573 = 120574 = 1 Since image statistical features and

distortions are usually space-variant authors of [60] employ

the SSIM index locally instead of globally Another reason for

this is that by applying the SSIM index locally a quality map

of the image which conveys more information about the

quality degradation can be generated

TABLE I SAMPLE TEN SUBJECT‟S FSIM VALUES WITH RESPECT TO EACH OTHER

Subject No

11 12 13 14 15 16 17 18 19 20

11 9342 7906 7438 7442 7648 7566 7509 78 7441 7597

12 7906 9523 734 7135 7459 745 7394 7505 7335 7449

13 7438 734 9705 743 7943 7264 776 7417 7941 7735

14 7442 7135 743 9429 8081 7252 7428 7478 7604 7406

15 7648 7459 7943 8081 943 7734 818 7903 834 8126

16 7566 745 7264 7252 7734 9247 7599 8769 7523 7713

17 7509 7394 776 7428 8189 7599 934 7552 8102 8612

18 7801 7505 7417 7478 7903 8769 7552 9342 7631 7669

19 7441 7335 7941 7604 834 7523 8102 7631 9693 806

20 7597 7449 7735 7464 8126 7713 8612 7669 806 9479

International Journal of Pure and Applied Mathematics Special Issue

141

TABLE II SAMPLE TEN SUBJECT‟S SSIM VALUES WITH RESPECT TO EACH OTHER

Subject No

11 12 13 14 15 16 17 18 19 20

11 9044 7333 6507 6937 7054 7217 6717 7433 6588 6854

12 7333 9327 6249 6298 6574 6905 6357 6976 6258 6421

13 6507 6249 9643 6744 7311 6586 7173 671 7242 7014

14 6937 6298 6744 9155 7673 6857 6911 7007 7009 6874

15 7054 6574 7311 7673 9158 7325 7676 7475 7685 7621

16 7217 6905 6586 6857 7325 925 711 867 694 7189

17 6717 6357 7173 6911 7676 711 9147 7083 7443 822

18 7433 6976 671 7007 7475 867 7083 9236 7054 7145

19 6588 6258 7242 7009 7685 694 7443 7054 9495 7423

20 6854 6421 7014 6874 7621 7189 822 7145 7423 9251

IV EXPERIMENTAL RESULTS AND ANALYSIS

In this section the performance of IQA techniques like FSIM

and SSIM are evaluated The parameters required in the

proposed methods were set as n = 4 J = 4 σr = 05978 σθ =

06545 T1 = 085 T2 = 160 T3 = T4 = 200 and λ = 003

Besides the center frequencies of the log-Gabor filters at four

scales were set as 16 112 124 and 148 These parameters

were then fixed for all the following experiments conducted

We take twenty set of database in which each database

consists of around seventy images Each and every image is

taken as the reference image and measured the similarity with

all other images present and the results are tabulated for FSIM

in Table I whereas for SSIM the results are tabulated in Table

II The average similarity index for each and every database

for the FSIM and SSIM are given in Figure 7 The results

clearly indicate that similarity measure is a good sign of a

quality measure as well as good metric to identify the

similarity between the images The results also gave a clear

indication that FSIM overcomes the drawbacks of SSIM and

gave a good measurement when compared to the SSIM

Fig 7 Graphical representation of FSIM and SSIM average values of the

given database

V CONCLUSION AND FUTURE WORK

The proposed work implemented the similarity index

assessment of thermal images following the sequence of the

work g iven as follows Darwinian Particle Swarm

Optimization is used for image segmentation as a multi-

threshold technique which has overcome various drawbacks

like computational time feature selectivity stability and

feasibility DPSO is better when compared to other

conventional multi-threshold techniques like Otsu image

segmentation fuzzy clustering PSO and ant colony

optimization Active contour image segmentation was

performed which is based on the level set based segmentation

method of Mumford Shah model producing binary image The

CORF operator extracts the contour image using Difference of

Gaussians and hysteresis thresholding The similarities of the

results are compared using FSIM and SSIM FSIM

outperforms the results of SSIM The results are good enough

to show that Image Quality Assessment techniques are helpful

in the process of identificat ion and classification of subjects

The given below points can be considered as a future work (i)

The results can be compared with other IQA metrics and (ii)

The proposed approach need to be explored in the domain of

medical imaging and satellite communicat ion

REFERENCES

[1] W Zhao R Chellappa A Rosenfeld and P Phillips ldquoFace recognition

A literature surveyrdquo ACM Computer Survey vol 35 no 4 pp 399-458 December 2003

[2] T Bourlai A Ross C Chen and L Hornak A study on using mid-wave infrared imagesfor face recognition In Proc SPIE 2012

[3] R S Ghiass O Arandjelovic A Bendada and X Maldague Infrared face recognition a literature review In Proc International Joint Conference on Neural Networks pages2791-2800 2013

[4] Yufeng Zheng ldquoFace detection and eyeglasses detection for thermal face recognitionrdquo ISampTSPIE Electronic Imaging Conference 22-26 January 2012 in Burlingame California United States

[5] F J Prokoski R B Riedel and J S Coffin ldquoIdentification of individuals by means of facial thermographyrdquo in Proceedings of The IEEE 1992 International Carnahan Conference on Security Technology Crime Countermeasures Atlanta GA USA 14-16 Oct pp 120-125 IEEE 1992

[6] Cutler R ldquoFace recognition using infrared images and eigenfacesrdquo httpciteseeristpsueducutler96facehtml April 1996 visited July 2007

[7] Socolinsky D Selinger A ldquoA comparative analysis of face recognition performance with visible and thermal infrared imageryrdquo Proceedings of the International Conference o Pattern Recognition (ICPR02) vol2 p 40217 Quebec Canada August 2002

[8] Socolinsky D Selinger A Neuheisel J ldquoFace recognition with visible and thermal infrared imageryrdquo Computer Vision amp Image Understanding vol 91 p 72-114 2003

50

60

70

80

90

100

1 3 5 7 9 11 13 15 17 19

FS

IM a

nd

SS

IM V

alu

es

Subject No

FSIM

SSIM

International Journal of Pure and Applied Mathematics Special Issue

142

[9] H-W Tzeng H-C Lee and M-Y Chen The design of isotherm face recognition technique based on nostril localization In Proc International Conference on System Science and Engineering pages 82-86 2011

[10] O Arandjelovic R I Hammoud and R Cipolla Thermal and re ectance based personal identification methodology in challenging variable illuminations Pattern Recognition 43(5)1801-1813 2010

[11] T Jin C Shouming X Xiuzhen and J Gu Eyes localization in an infrared image In Proc IEEE International Conference on Automation and Logistics (ICAL) pages 217-222 2009

[12] T Bourlai and Z Jafri Eye detection in the middle-wave infrared spectrum Towards recognition in the dark In Proc IEEE International Workshop on Information Forensic and Security (WIFS) pages 1-6 2011

[13] B Martinez X Binefa and M Pantic Facial component detection in thermal imagery In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 48-54 2010

[14] Chen X Jing Z Xiao G ldquoFuzzy fusion for face recognitionrdquo Proceedings of the International Conference on Fuzzy Systems and Knowledge Discovery (FSKD05) p 672- 675 Changsha China August 2005

[15] S Zhao and R Grigat An automatic face recognition system in the near infrared spectrum MLDM pages 437-444 2005

[16] T Elguebaly and N Bouguila ldquoA Bayesian method for infrared face recognitionrdquo Machine Vision Beyond Visible Spectrum 2011

[17] Y Yoshitomi T Miyaura S Tomita and S Kimura Face identification using thermalimage processing RO-MAN pages 374-379 1997

[18] S Li R Chu M Ao L Zhang and R He Highly accurate and fast face recognitionusing near infrared images In Proc IAPR International Conference on Biometricspages 151-158 2006

[19] H Maeng H-C Choi U Park S-W Lee and A K Jain NFRAD Near-infraredface recognition at a distance In Proc International Joint Conference on Biometrics(IJCB) pages 1-7 2011

[20] D Goswami C H Chan D Windridge and J Kittler Evaluation of face recognition system in heterogeneous environments (visible vs NIR) In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 2160-2167 2011

[21] A Srivastana and X Liu Statistical hypothesis pruning for recognizing faces from infrared images Image and Vision Computing 21(7)651-661 2003

[22] Z Xie SWu G Liu and Z Fang Infrared face recognition based on radiant energy and curvelet transformation In Proc International Conference on Information Assurance and Security (IAS) 2215-218 2009

[23] P Buddharaju I Pavlidis and P Tsiamyrtzis Pose-invariant physiological face recognition in the thermal infrared spectrum In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 53-60 2006

[24] P Buddharaju and I Pavlidis Physiological face recognition is coming of age In Proc IEEE Conference on Computer Vision and Pattern Recognition pages 128-135 2009

[25] T R Gault N Blumenthal A A Farag and T Starr Extraction of the superficial facial vasculature vital signs waveforms and rates using thermal imaging In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 1-8 2010

[26] A Seal M Nasipuri D Bhattacharjee and DK Basu Minutiae based thermal face recognition using blood perfusion data International Conference on Image Information Processing pages 1-4 2011

[27] S Cho L Wang and W J Ong Thermal imprint feature analysis for face recognitionISIE pages 1875-1880 2009

[28] R S Ghiass O Arandjelovic A Bendada and X Maldague Vesselness features and the inverse compositional AAM for robust face recognition using thermal IR In Proc AAAI Conference on Artificial Intelligence pages 357-364 2013

[29] S Wu Z Gu K A Chia and S H Ong Infrared facial recognition using modified blood perfusion ICICS pages 1-5 2007

[30] Z Xie S Wu G Liu and Z Fang Infrared face recognition method based on blood perfusion image and curvelet transformation In Proc

International Conference on Wavelet Analysis and Pattern Recognition pages 360-364 2009

[31] Kennedy J amp Eberhart R ldquoA new optimizer using particle swarm theoryrdquo in Proceedings of the IEEE sixth international symposium on micro machine andhuman science pp 39ndash43 1995

[32] Tillett J Rao T M Sahin F Rao R amp Brockport S (2005) Darwinian Particle Swarm Optimization In Proceedings of the 2nd Indian international conference onartificial intelligence (pp 1474ndash1487)

[33] Z Chenglin S Xuebin S Songlin and J Ting ldquoFault diagnosis of sensor by chaos particle swarm optimization algorithm and support vector machinerdquo Expert Systems with Applications vol 38 no 8 pp 9908ndash9912 2011

[34] P Ghamisi M S Couceiro J A Benediktsson and N M F Ferreira An Efficient Method for Segmentation of Images Based on Fractional Calculus and Natural Selection Expert Systems With Applications vol 39 no 16 pp 12407- 2417 Nov 2012

[35] P Ghamisi M S Couceiro F M L Martins and J A Benediktsson Multi-level Image Segmentation Based on Fractional-Order Darwinian Particle Swarm Optimization IEEE Transactions on Geoscience and Remote Sensing vol 52 no 5 pp 2382-2394 May 2014

[36] M S Couceiro N M F Ferreira and J A T Machado ldquoFractional order Darwinian particle swarm optimizationrdquo in proc Symp FSS Coimbra Portugal pp 4-5 Nov 2011

[37] P Ghamisi M S Couceiro and J A Benediktsson Classification of Hyperspectral Images with Binary Fractional Order Darwinian PSO and Random Forests in Proc SPIE Image and Signal Processing for Remote Sensing XIX 2013

[38] G Majumder and M K Bhowmik ldquoGabor-Fast ICA feature extraction for thermal face recognition using linear kernel support vector machinerdquo Computational Intelligence and Networks (CINE) 2015 International Conference on DOI 101109CINE201514 pp21 ndash 25 2015

[39] T Chan L Vese and Y Sandberg Active contours without edges for vector-valued images Journal of Visual Communications and Image Representation 11 no 2 (2000) pp 130-141

[40] D Mumford and J Shah Optimal approximation by piecewise smooth functions and associated variational problems Comm Pure Appl Math 42 1989 pp 577-685

[41] M Sussman P Smereka and S Osher A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow J Comput Phys V 119 (1994) pp 146-159

[42] L Vese and T Chan A multiphase level set framework for image segmentation using the mumford and shah model International Journal of Computer Vision vol 50 pp 271-293 2002

[43] T F Chan and L A Vese Image segmentation using level sets and the piecewise-constant Mumford-Shah model 2000

[44] D Cremers F R Schmidt and F Barthel Shape priors in variational image segmentation Convexity lipschitz continuity and globally optimal solutions in Computer Vision and Pattern Recognition 2008 CVPR 2008 IEEE Conference on 2008 pp 1-6

[45] S Osher and J A Sethian Fronts propagating with curvature-dependent speed algorithms based on Hamilton-Jacobi formulations Journal of computat ional physics vol 79 pp 12-49 1988

[46] R Ronfard Region-based strategies for active contour models International Journal of Computer Vision vol 13 pp 229-251 1994

[47] K Siddiqi Y B Lauziere A Tannenbaum and S W Zucker Area and length minimizing flows for shape segmentation Image Processing IEEE Transactions on vol 7 pp 433-443 1998

[48] Cosmin Grigorescu Nicolai Petkov Michel A Westenberg Contour and boundary detection improved by surround suppression of texture edges Image and Vision Computing Vol 22 pp 609-622 2004

[49] Azzopardi G Petkov N A CORF computational model of a simple cell that relies on LGN input outperforms the Gabor function model Biol Cybern 106(3) 177ndash189 (2012)

[50] Azzopardi G Petkov N Contour detection by CORF operator In Villa AEP Duch W Erdi P Masulli F Palm G (eds) ICANN 2012 Part I LNCS vol acute 7552 pp 395ndash402 Springer Heidelberg (2012)

International Journal of Pure and Applied Mathematics Special Issue

143

[51] Z Wang AC Bovik HR Sheikh and EP Simoncelli ldquoImage quality assessment from error visibility to structural similarityrdquo IEEE Trans Image Process vol 13 no 4 pp 600-612 Apr 2004

[52] Lin Zhang Lei Zhang Xuanqin Mou and David Zhang FSIM a feature similarity index for image quality assessment IEEE Transactions on Image Processing vol 20 no 8 pp 2378-2386 2011

[53] P Kovesi ldquoImage features from phase congruencyrdquo Videre J Comp Vis Res vol 1 no 3 pp 1-26 1999

[54] L Henriksson A Hyvaumlrinen and S Vanni ldquoRepresentation of cross-frequency spatial phase relationships in human visual cortexrdquo J Neuroscience vol 29 no 45 pp 14342-14351 Nov 2009

[55] C Mancas-Thillou and B Gosselin ldquoCharacter segmentation-by-recognition using log-Gabor filtersrdquo in Proc Int Conf Pattern Recognit 2006 pp 901-904

[56] S Fischer F Šroubek L Perrinet R Redondo and G Cristoacutebal ldquoSelf-invertible 2D log-Gabor waveletsrdquo Int J Computer Vision vol 75 no 2 pp 231-246 Nov 2007

[57] W Wang J Li F Huang and H Feng ldquoDesign and implementation of log-Gabor filter in fingerprint image enhancementrdquo Pattern Recognit Letters vol 29 no 3 pp 301-308 Feb 2008

[58] H R Sheikh and A C Bovik Image information and visual quality IEEE Trans Image Processing vol 15 pp 430-444 Feb 2006

[59] Z Wang Rate scalable foveated image and video communications PhD thesis Dept of ECE the University of Texas at Austin Dec 2001

[60] Z Wang and A C Bovik A universal image quality index IEEE Signal Processing Letters vol 9 pp 81-84 March 2002

International Journal of Pure and Applied Mathematics Special Issue

144

145

146

The last term in the regularizat ion is used to encourage

smooth short contours [47] The force term can be expressed

simply as

119864119877119890119892119906119897119886119903119894119911119886119905119894119900119899 empty119894 119909119910 = 120575 empty119894 119909119910 |nablaempty119894 119909119910 |119889119909119889119910 (13)

The results of the active contour image segmentation are

displayed in Figure 3 and histogram representations are given

in Figure 4

Fig 3 Top row DPSO segmented images Bottom row Active contour

segmented images

Fig 4 (a) Thermal image(b) Histogram representation of thermal image (c) DPSO segmented image (d) DPSO segmented histogram representation (e) Active contour segmented image (f) Histogram of Active contour image

C CORF edge detector

The implementation of the proposed CORF operator is rather

straightforward it includes blurring (achieved by convolving

with a Gaussian function) of halfwave rectified responses of

DoG operators shifting appropriately these blurred res ponses

by different vectors which are determined in the configuration

of the operator and using them for the pixel-wise evaluation

of a weighted geometric mean that gives the output of the

CORF operatorWe apply a classical two-step procedure in

computer vision thatwas proposed by [48] and [49] to obtain a

binary contour mapfrom the output of the concerned model

The first step consists ofedge thinning by non-maximum

suppression to determine theridges in the given response

image Then we apply hysteresis thresholding to obtain a

binary contour map The latter steprequires a high and a low

threshold value Similar to the work in[50] we set the low

threshold value to a fraction (05) of the highthreshold For a

given image we set the high threshold to be thelowest value

of the strongest f pixels in the thinned responseimage The

given value of the parameter f is a fraction of the totalnumber

of pixels in the image The resulting binary map containsthe

strongest fraction f of contour pixels together with

anyconnected ones that are achieved by hysteresis

thresholding The parameters used for the CORF operator are

the number of orientations nϴ (n=12 for ϴ=П6) a scale

parameter σ wavelength λ= σ4 and a spatial aspect ratio

γ=05

(i) Non-maximum suppression edge thinning

TheNon-maxima suppression thins the areas in which

119862120590 119909 119910 is non-zero to one-pixel wide candidate contours as

follows For each position 119909 119910 two responses Cσ(x|y

|) and

Cσ(x||y

||) in adjacent positions (x

|y

|) and (x

||y

||) that are

intersection points of a line passing through 119909 119910 in

orientation 120579120590 119909 119910 and a square defined by the diagonal

points of an 8-neighbourhood are computed by linear

interpolation as given by Figure 5 If the response

119862120590 119909 119910 at 119909 119910 is greater than both these values (ie it is a

local maximumalong the concerned line) it is retained

otherwise it isassigned the value zero

Fig 5 Interpolated responses at positions (x|y

|) and (x

||y

||) Non-

maximasuppression retains the value in the central pixel ethx yTHORN if it is larger

than thevalues at (x|y

|) and (x

||y

||)

Fig 6 (a) Image after active contour segmentation (b) One pixel binarized hysteresis threshold image (c) Image after CORF edge detection

International Journal of Pure and Applied Mathematics Special Issue

139

ii) Binarizat ion by Hysteresis thresholding

Next a binary map is computed from the candidate contour

pixels by hysteresis thresholding This process involves two

threshold values TLand TH TLltTH Commonly the high

threshold value THis computed as a (1-p)-quantile of the

distribution of the response values at the candidate contour

pixels where p is the minimum fraction of candidate pixels to

be retained in the contour map Candidate contour pixels with

responses higher than th are definitely retained in the contour

map while the ones with responses below the low threshold

TLare discarded Candidate contour pixels with responses

between TLand THare retained if they can be connected to any

candidate contour pixel with a response higher than THthrough

a chain of other candidate contour pixels with responses larger

than TL Figure 6 gives the results of edge thinning by non-

maximum suppression to one pixel and CORF edge detection

by hysteresis thresholding

D FSIM and SSIM

The aim of objective Image Quality Assessment (IQA) is to

develop mathemat ical models that are able to forecast the

quality of an image precisely and spontaneously An ideal

objective IQA method should be able to simulate the quality

predictions of an average human observer The proper IQA

method calculates the similarity index using a mathemat ical

model by quantizing the distortion image and the reference

image The main feature of the proper IQA is that it can be

embedded in real t ime image processing system The most

advanced method to perform IQA is Structure Similarity Index

Measurement (SSIM) [51] The various features like

luminance contrast and structure are compared in the SSIM

Almost all these features are consistent with the Human

Visual System (HVS) and are compatible But there are few

drawbacks as the luminance and contrast are sensitive to the

illumination To overcome the drawbacks of the

aforementioned technique Feature Similarity Index

Measurement (FSIM) has come into existence [52] In FSIM

two features main ly Phase Congruency (PC) [53] [54] and

Gradient Magnitude (GM) are considered To compute the PC

of 2D grayscale images The 1D log-Gabor filters described

earlier can be extended to 2D ones by simply applying some

spreading function across thefilter perpendicular to its

orientation One widely used spreading functionis Gaussian

[55] [56] and [57] By using Gaussian as the spreading

function the 2D log-Gabor function has the following transfer

function

1198662 120596120579119895 = 119890119909119901 119897119900119892 120596 1205960

2

21205901199032

119890119909119901 120579minus120579119895

2

21205901205792

(14)

Where 120579119895 = 119895120587 119869 119895 = 01hellip 119869 minus 1 the orientation angle of

the filter is 119869 is the number of orientations and 120590120579determines

the filter‟s angular bandwidthBy modulat ing 120596120579 and 120579119895 and

convolving 1198662with the 2D image we get a set of responses at

each point x as 119890119899120579119895 119883 119874119899 120579119895

119883 The local amplitude on

scale n and orientation 120579119895is119860119899120579119895 119883 = 119890119899 120579119895

119883 2 +119874119899 120579119895 119883 2

and the local energy along orientation 120579119895 is119864120579119895 119883 =

119865120579119895 119883 2 + 119867120579119895

119883 2 where119865120579119895 119883 = 119890119899 120579119895

119883 119899 and

119867120579119895 119883 = 119900119899 120579119895

119883 119899 The 2D PC at x is defined as

1198751198622119863 119883 = 119864120579 119895

119883 119895

휀+ 119860119899 120579 119895 119883 119895119899

(15)

It should be noted that 1198751198622119863 119883 is a real number within 0~1

(i) The FS IM index

The computation of FSIM index consists of two stages In the

first stage the local similarity map is computed and then in

the second stage we pool the similarity map into a single

similarity score We separate the feature similarity

measurement between 1198911 119883 and 1198912 119883 into two

components each for PC or GM First the similarity measure

for 1198751198621 119883 and 1198751198622 119883 is defined as

119878119875119862 119883 =21198751198621 119883 1198751198622 119883 +1198791

11987511986212 119883 +1198751198622

2 119883 +1198791 (16)

where 1198791 is a positive constant to increase the stability of SPC

(such a consideration was also included in SSIM [51]) In practice the determination of 1198791 depends on the dynamic

range of PC values Equation 16 is a commonly used measure

to define the similarity of two positive real numbers and its

result ranges within [0 1] Similarly the GM values 1198661 119883

and 1198662 119883 are compared and the similarity measure is defined

as

119878119866 119883 =21198661 119883 1198662 119883 +1198792

11986612 119883 +1198662

2 119883 +1198792 (17)

where 1198792 is a positive constant depending on the dynamic

range of GM values In our experiments both 1198791 and 1198792 will

be fixed to all databases so that the proposed FSIM can be conveniently used Then 119878119875119862 119883 and 119878119866 119883 are combined to

get the similarity 119878119871 119883 of 1198911 119883 and 1198912 119883 We define

119878119871 119883 as

119878119871 119883 = 119878119875119862 119883 120572

119878119866 119883 120573

(18)

where 120572 and 120573 are parameters used to adjust the relative

importance of PC and GM features In this paper we set 120572 = 120573 =1 for simplicity Thus119878119871 119883 = 119878119875119862 119883 119878119866 119883 Having

obtained the similarity 119878119871 119883 at each location 119883 the overall

similarity between 1198911and 1198912 can becalculated However

different locations have different contributions to HVS‟

perception of the image For example edge locations convey

more crucial v isual information than the locations within a

smooth area Since human visual cortex is sensitive to phase

congruent structures [54] the PC value at a location canreflect

how likely it is a perceptibly significant structure point Intuitively for a given location 119883 if anyone of 1198911 119883 and

1198912 119883 has a significant PC value it implies that this position x

International Journal of Pure and Applied Mathematics Special Issue

140

will have a high impact on HVS in evaluating the similarity between 1198911 and 1198912 Therefore we use 119875119862119898 119883 =

max(1198751198621 119883 1198751198622 119883 ) to weight the importance of 119878119871 119883 in

the overall similarity between 1198911 and 1198912 and accordingly the

FSIM index between 1198911and 1198912 is defined as

119865119878119868119872 = 119878119871 119883 119883 isinΩ 119875119862119898 119883

119875119862119898 119883 119883isinΩ (19)

where Ω means the whole image spatial domain

(ii) Structural similarity index (SSIM)

The SSIM algorithm performs similarity measurement in three

steps luminance comparison contrast comparison and

structure comparison First the luminance of each image

signal is compared The estimated mean intensity is computed

as follows

120583119903119890119891 =1

119882119867 119868119903119890119891 119894 119895

119882119894 = 1

119867119895 = 1 (20)

The luminance comparison function 119897 119868119903119890119891 119868119905119904119905 is a

function of 120583119903119890119891 and 120583119905119904119905Second the contrast of each image

signal is compared For estimat ing the contrast standard

deviation is being used An unbiased estimate of standard

deviation in discrete form is as follows 120590119903119890119891

= 1

119882119867minus1 119868119903119890119891 119894 119895 minus 120583119903119890119891

2119882119894 = 1

119867119895 = 1

1

2

(21)

The contrast comparison function 119888 119868119903119890119891 119868119905119904119905 is a function

of120590119903119890119891 and 120590119905119904119905 Third the structure of each image signal is

compared Structure comparison function119904 119868119903119890119891 119868119905119904119905 is a

function of 119868119903119890119891 minus 120583119903119890119891 120590119903119890119891 and

119868119905119904119905 minus 120583119905119904119905 120590119905119904119905 Finally three comparison functions are

combined and an overall similarity measure is produced The

overall similarity measure119878 119868119903119890119891 119868119905119904119905 is a function of

119897 119868119903119890119891 119868119905119904119905 119888 119868119903119890119891 119868119905119904119905 119888 119868119903119890119891 119868119905119904119905 and 119904 119868119903119890119891 119868119905119904119905

Definitions of119897 119868119903119890119891 119868119905119904119905 119888 119868119903119890119891 119868119905119904119905 and119904 119868119903119890119891 119868119905119904119905 are as

follows

For luminance comparison function we have

119904 119868119903119890119891 119868119905119904119905 =2120583119903119890119891 120583119905119904119905 +1198791

1205831199031198901198912 +120583119905119904119905

2 +1198791 (21)

where 1198791 is a positive stabilizing constant chosen to prevent

the denominator from becoming too small We have

1198791 = 1199051119863 2 (22)

where D is the dynamic range of pixel values and 1199051 ltlt 1 is

a small constant For contrast comparison function we have

119888 119868119903119890119891 119868119905119904119905 =2120590119903119890119891 120590119905119904119905 +1198792

1205901199031198901198912 +120590119905119904119905

2 +1198792 (23)

where 1198792 = 1199052119863 2is a positive stabilizing constant

And1199052 ltlt 1 For structure comparison function we have

119904 119868119903119890119891 119868119905119904119905 =120590119903119890119891 119905119904119905+1198793

120590119903119890119891 120590119905119904119905 +1198793 (24)

where 1198793 is a positive stabilizing constant In (58)120590119903119890119891 119905119904119905 is

the correlation coefficient between the reference and test images In the discrete form120590119903119890119891 119905119904119905 can be estimated by

120590119903119890119891 119905119904119905 =1

119882119867minus1 119868119903119890119891 119894 119895 minus 120583119903119890119891 119868119905119904119905 119894 119895 minus

119882119894 = 1

119867119895 = 1

120583119905119904119905 (25)

Finally structural similarity index is defined as

119878119878119868119872 119868119903119890119891 119868119905119904119905 =

119897 119868119903119890119891 119868119905119904119905 120572 119888 119868119903119890119891 119868119905119904119905

120573 119904 119868119903119890119891 119868119905119904119905

120574 (26)

where 120572 120573 and 120574The universal quality index (UQI) [5960] is a special case of the SSIM index when1198791 = 1198792 = 1198793 = 0

and 120572 = 120573 = 120574 = 1 Since image statistical features and

distortions are usually space-variant authors of [60] employ

the SSIM index locally instead of globally Another reason for

this is that by applying the SSIM index locally a quality map

of the image which conveys more information about the

quality degradation can be generated

TABLE I SAMPLE TEN SUBJECT‟S FSIM VALUES WITH RESPECT TO EACH OTHER

Subject No

11 12 13 14 15 16 17 18 19 20

11 9342 7906 7438 7442 7648 7566 7509 78 7441 7597

12 7906 9523 734 7135 7459 745 7394 7505 7335 7449

13 7438 734 9705 743 7943 7264 776 7417 7941 7735

14 7442 7135 743 9429 8081 7252 7428 7478 7604 7406

15 7648 7459 7943 8081 943 7734 818 7903 834 8126

16 7566 745 7264 7252 7734 9247 7599 8769 7523 7713

17 7509 7394 776 7428 8189 7599 934 7552 8102 8612

18 7801 7505 7417 7478 7903 8769 7552 9342 7631 7669

19 7441 7335 7941 7604 834 7523 8102 7631 9693 806

20 7597 7449 7735 7464 8126 7713 8612 7669 806 9479

International Journal of Pure and Applied Mathematics Special Issue

141

TABLE II SAMPLE TEN SUBJECT‟S SSIM VALUES WITH RESPECT TO EACH OTHER

Subject No

11 12 13 14 15 16 17 18 19 20

11 9044 7333 6507 6937 7054 7217 6717 7433 6588 6854

12 7333 9327 6249 6298 6574 6905 6357 6976 6258 6421

13 6507 6249 9643 6744 7311 6586 7173 671 7242 7014

14 6937 6298 6744 9155 7673 6857 6911 7007 7009 6874

15 7054 6574 7311 7673 9158 7325 7676 7475 7685 7621

16 7217 6905 6586 6857 7325 925 711 867 694 7189

17 6717 6357 7173 6911 7676 711 9147 7083 7443 822

18 7433 6976 671 7007 7475 867 7083 9236 7054 7145

19 6588 6258 7242 7009 7685 694 7443 7054 9495 7423

20 6854 6421 7014 6874 7621 7189 822 7145 7423 9251

IV EXPERIMENTAL RESULTS AND ANALYSIS

In this section the performance of IQA techniques like FSIM

and SSIM are evaluated The parameters required in the

proposed methods were set as n = 4 J = 4 σr = 05978 σθ =

06545 T1 = 085 T2 = 160 T3 = T4 = 200 and λ = 003

Besides the center frequencies of the log-Gabor filters at four

scales were set as 16 112 124 and 148 These parameters

were then fixed for all the following experiments conducted

We take twenty set of database in which each database

consists of around seventy images Each and every image is

taken as the reference image and measured the similarity with

all other images present and the results are tabulated for FSIM

in Table I whereas for SSIM the results are tabulated in Table

II The average similarity index for each and every database

for the FSIM and SSIM are given in Figure 7 The results

clearly indicate that similarity measure is a good sign of a

quality measure as well as good metric to identify the

similarity between the images The results also gave a clear

indication that FSIM overcomes the drawbacks of SSIM and

gave a good measurement when compared to the SSIM

Fig 7 Graphical representation of FSIM and SSIM average values of the

given database

V CONCLUSION AND FUTURE WORK

The proposed work implemented the similarity index

assessment of thermal images following the sequence of the

work g iven as follows Darwinian Particle Swarm

Optimization is used for image segmentation as a multi-

threshold technique which has overcome various drawbacks

like computational time feature selectivity stability and

feasibility DPSO is better when compared to other

conventional multi-threshold techniques like Otsu image

segmentation fuzzy clustering PSO and ant colony

optimization Active contour image segmentation was

performed which is based on the level set based segmentation

method of Mumford Shah model producing binary image The

CORF operator extracts the contour image using Difference of

Gaussians and hysteresis thresholding The similarities of the

results are compared using FSIM and SSIM FSIM

outperforms the results of SSIM The results are good enough

to show that Image Quality Assessment techniques are helpful

in the process of identificat ion and classification of subjects

The given below points can be considered as a future work (i)

The results can be compared with other IQA metrics and (ii)

The proposed approach need to be explored in the domain of

medical imaging and satellite communicat ion

REFERENCES

[1] W Zhao R Chellappa A Rosenfeld and P Phillips ldquoFace recognition

A literature surveyrdquo ACM Computer Survey vol 35 no 4 pp 399-458 December 2003

[2] T Bourlai A Ross C Chen and L Hornak A study on using mid-wave infrared imagesfor face recognition In Proc SPIE 2012

[3] R S Ghiass O Arandjelovic A Bendada and X Maldague Infrared face recognition a literature review In Proc International Joint Conference on Neural Networks pages2791-2800 2013

[4] Yufeng Zheng ldquoFace detection and eyeglasses detection for thermal face recognitionrdquo ISampTSPIE Electronic Imaging Conference 22-26 January 2012 in Burlingame California United States

[5] F J Prokoski R B Riedel and J S Coffin ldquoIdentification of individuals by means of facial thermographyrdquo in Proceedings of The IEEE 1992 International Carnahan Conference on Security Technology Crime Countermeasures Atlanta GA USA 14-16 Oct pp 120-125 IEEE 1992

[6] Cutler R ldquoFace recognition using infrared images and eigenfacesrdquo httpciteseeristpsueducutler96facehtml April 1996 visited July 2007

[7] Socolinsky D Selinger A ldquoA comparative analysis of face recognition performance with visible and thermal infrared imageryrdquo Proceedings of the International Conference o Pattern Recognition (ICPR02) vol2 p 40217 Quebec Canada August 2002

[8] Socolinsky D Selinger A Neuheisel J ldquoFace recognition with visible and thermal infrared imageryrdquo Computer Vision amp Image Understanding vol 91 p 72-114 2003

50

60

70

80

90

100

1 3 5 7 9 11 13 15 17 19

FS

IM a

nd

SS

IM V

alu

es

Subject No

FSIM

SSIM

International Journal of Pure and Applied Mathematics Special Issue

142

[9] H-W Tzeng H-C Lee and M-Y Chen The design of isotherm face recognition technique based on nostril localization In Proc International Conference on System Science and Engineering pages 82-86 2011

[10] O Arandjelovic R I Hammoud and R Cipolla Thermal and re ectance based personal identification methodology in challenging variable illuminations Pattern Recognition 43(5)1801-1813 2010

[11] T Jin C Shouming X Xiuzhen and J Gu Eyes localization in an infrared image In Proc IEEE International Conference on Automation and Logistics (ICAL) pages 217-222 2009

[12] T Bourlai and Z Jafri Eye detection in the middle-wave infrared spectrum Towards recognition in the dark In Proc IEEE International Workshop on Information Forensic and Security (WIFS) pages 1-6 2011

[13] B Martinez X Binefa and M Pantic Facial component detection in thermal imagery In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 48-54 2010

[14] Chen X Jing Z Xiao G ldquoFuzzy fusion for face recognitionrdquo Proceedings of the International Conference on Fuzzy Systems and Knowledge Discovery (FSKD05) p 672- 675 Changsha China August 2005

[15] S Zhao and R Grigat An automatic face recognition system in the near infrared spectrum MLDM pages 437-444 2005

[16] T Elguebaly and N Bouguila ldquoA Bayesian method for infrared face recognitionrdquo Machine Vision Beyond Visible Spectrum 2011

[17] Y Yoshitomi T Miyaura S Tomita and S Kimura Face identification using thermalimage processing RO-MAN pages 374-379 1997

[18] S Li R Chu M Ao L Zhang and R He Highly accurate and fast face recognitionusing near infrared images In Proc IAPR International Conference on Biometricspages 151-158 2006

[19] H Maeng H-C Choi U Park S-W Lee and A K Jain NFRAD Near-infraredface recognition at a distance In Proc International Joint Conference on Biometrics(IJCB) pages 1-7 2011

[20] D Goswami C H Chan D Windridge and J Kittler Evaluation of face recognition system in heterogeneous environments (visible vs NIR) In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 2160-2167 2011

[21] A Srivastana and X Liu Statistical hypothesis pruning for recognizing faces from infrared images Image and Vision Computing 21(7)651-661 2003

[22] Z Xie SWu G Liu and Z Fang Infrared face recognition based on radiant energy and curvelet transformation In Proc International Conference on Information Assurance and Security (IAS) 2215-218 2009

[23] P Buddharaju I Pavlidis and P Tsiamyrtzis Pose-invariant physiological face recognition in the thermal infrared spectrum In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 53-60 2006

[24] P Buddharaju and I Pavlidis Physiological face recognition is coming of age In Proc IEEE Conference on Computer Vision and Pattern Recognition pages 128-135 2009

[25] T R Gault N Blumenthal A A Farag and T Starr Extraction of the superficial facial vasculature vital signs waveforms and rates using thermal imaging In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 1-8 2010

[26] A Seal M Nasipuri D Bhattacharjee and DK Basu Minutiae based thermal face recognition using blood perfusion data International Conference on Image Information Processing pages 1-4 2011

[27] S Cho L Wang and W J Ong Thermal imprint feature analysis for face recognitionISIE pages 1875-1880 2009

[28] R S Ghiass O Arandjelovic A Bendada and X Maldague Vesselness features and the inverse compositional AAM for robust face recognition using thermal IR In Proc AAAI Conference on Artificial Intelligence pages 357-364 2013

[29] S Wu Z Gu K A Chia and S H Ong Infrared facial recognition using modified blood perfusion ICICS pages 1-5 2007

[30] Z Xie S Wu G Liu and Z Fang Infrared face recognition method based on blood perfusion image and curvelet transformation In Proc

International Conference on Wavelet Analysis and Pattern Recognition pages 360-364 2009

[31] Kennedy J amp Eberhart R ldquoA new optimizer using particle swarm theoryrdquo in Proceedings of the IEEE sixth international symposium on micro machine andhuman science pp 39ndash43 1995

[32] Tillett J Rao T M Sahin F Rao R amp Brockport S (2005) Darwinian Particle Swarm Optimization In Proceedings of the 2nd Indian international conference onartificial intelligence (pp 1474ndash1487)

[33] Z Chenglin S Xuebin S Songlin and J Ting ldquoFault diagnosis of sensor by chaos particle swarm optimization algorithm and support vector machinerdquo Expert Systems with Applications vol 38 no 8 pp 9908ndash9912 2011

[34] P Ghamisi M S Couceiro J A Benediktsson and N M F Ferreira An Efficient Method for Segmentation of Images Based on Fractional Calculus and Natural Selection Expert Systems With Applications vol 39 no 16 pp 12407- 2417 Nov 2012

[35] P Ghamisi M S Couceiro F M L Martins and J A Benediktsson Multi-level Image Segmentation Based on Fractional-Order Darwinian Particle Swarm Optimization IEEE Transactions on Geoscience and Remote Sensing vol 52 no 5 pp 2382-2394 May 2014

[36] M S Couceiro N M F Ferreira and J A T Machado ldquoFractional order Darwinian particle swarm optimizationrdquo in proc Symp FSS Coimbra Portugal pp 4-5 Nov 2011

[37] P Ghamisi M S Couceiro and J A Benediktsson Classification of Hyperspectral Images with Binary Fractional Order Darwinian PSO and Random Forests in Proc SPIE Image and Signal Processing for Remote Sensing XIX 2013

[38] G Majumder and M K Bhowmik ldquoGabor-Fast ICA feature extraction for thermal face recognition using linear kernel support vector machinerdquo Computational Intelligence and Networks (CINE) 2015 International Conference on DOI 101109CINE201514 pp21 ndash 25 2015

[39] T Chan L Vese and Y Sandberg Active contours without edges for vector-valued images Journal of Visual Communications and Image Representation 11 no 2 (2000) pp 130-141

[40] D Mumford and J Shah Optimal approximation by piecewise smooth functions and associated variational problems Comm Pure Appl Math 42 1989 pp 577-685

[41] M Sussman P Smereka and S Osher A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow J Comput Phys V 119 (1994) pp 146-159

[42] L Vese and T Chan A multiphase level set framework for image segmentation using the mumford and shah model International Journal of Computer Vision vol 50 pp 271-293 2002

[43] T F Chan and L A Vese Image segmentation using level sets and the piecewise-constant Mumford-Shah model 2000

[44] D Cremers F R Schmidt and F Barthel Shape priors in variational image segmentation Convexity lipschitz continuity and globally optimal solutions in Computer Vision and Pattern Recognition 2008 CVPR 2008 IEEE Conference on 2008 pp 1-6

[45] S Osher and J A Sethian Fronts propagating with curvature-dependent speed algorithms based on Hamilton-Jacobi formulations Journal of computat ional physics vol 79 pp 12-49 1988

[46] R Ronfard Region-based strategies for active contour models International Journal of Computer Vision vol 13 pp 229-251 1994

[47] K Siddiqi Y B Lauziere A Tannenbaum and S W Zucker Area and length minimizing flows for shape segmentation Image Processing IEEE Transactions on vol 7 pp 433-443 1998

[48] Cosmin Grigorescu Nicolai Petkov Michel A Westenberg Contour and boundary detection improved by surround suppression of texture edges Image and Vision Computing Vol 22 pp 609-622 2004

[49] Azzopardi G Petkov N A CORF computational model of a simple cell that relies on LGN input outperforms the Gabor function model Biol Cybern 106(3) 177ndash189 (2012)

[50] Azzopardi G Petkov N Contour detection by CORF operator In Villa AEP Duch W Erdi P Masulli F Palm G (eds) ICANN 2012 Part I LNCS vol acute 7552 pp 395ndash402 Springer Heidelberg (2012)

International Journal of Pure and Applied Mathematics Special Issue

143

[51] Z Wang AC Bovik HR Sheikh and EP Simoncelli ldquoImage quality assessment from error visibility to structural similarityrdquo IEEE Trans Image Process vol 13 no 4 pp 600-612 Apr 2004

[52] Lin Zhang Lei Zhang Xuanqin Mou and David Zhang FSIM a feature similarity index for image quality assessment IEEE Transactions on Image Processing vol 20 no 8 pp 2378-2386 2011

[53] P Kovesi ldquoImage features from phase congruencyrdquo Videre J Comp Vis Res vol 1 no 3 pp 1-26 1999

[54] L Henriksson A Hyvaumlrinen and S Vanni ldquoRepresentation of cross-frequency spatial phase relationships in human visual cortexrdquo J Neuroscience vol 29 no 45 pp 14342-14351 Nov 2009

[55] C Mancas-Thillou and B Gosselin ldquoCharacter segmentation-by-recognition using log-Gabor filtersrdquo in Proc Int Conf Pattern Recognit 2006 pp 901-904

[56] S Fischer F Šroubek L Perrinet R Redondo and G Cristoacutebal ldquoSelf-invertible 2D log-Gabor waveletsrdquo Int J Computer Vision vol 75 no 2 pp 231-246 Nov 2007

[57] W Wang J Li F Huang and H Feng ldquoDesign and implementation of log-Gabor filter in fingerprint image enhancementrdquo Pattern Recognit Letters vol 29 no 3 pp 301-308 Feb 2008

[58] H R Sheikh and A C Bovik Image information and visual quality IEEE Trans Image Processing vol 15 pp 430-444 Feb 2006

[59] Z Wang Rate scalable foveated image and video communications PhD thesis Dept of ECE the University of Texas at Austin Dec 2001

[60] Z Wang and A C Bovik A universal image quality index IEEE Signal Processing Letters vol 9 pp 81-84 March 2002

International Journal of Pure and Applied Mathematics Special Issue

144

145

146

ii) Binarizat ion by Hysteresis thresholding

Next a binary map is computed from the candidate contour

pixels by hysteresis thresholding This process involves two

threshold values TLand TH TLltTH Commonly the high

threshold value THis computed as a (1-p)-quantile of the

distribution of the response values at the candidate contour

pixels where p is the minimum fraction of candidate pixels to

be retained in the contour map Candidate contour pixels with

responses higher than th are definitely retained in the contour

map while the ones with responses below the low threshold

TLare discarded Candidate contour pixels with responses

between TLand THare retained if they can be connected to any

candidate contour pixel with a response higher than THthrough

a chain of other candidate contour pixels with responses larger

than TL Figure 6 gives the results of edge thinning by non-

maximum suppression to one pixel and CORF edge detection

by hysteresis thresholding

D FSIM and SSIM

The aim of objective Image Quality Assessment (IQA) is to

develop mathemat ical models that are able to forecast the

quality of an image precisely and spontaneously An ideal

objective IQA method should be able to simulate the quality

predictions of an average human observer The proper IQA

method calculates the similarity index using a mathemat ical

model by quantizing the distortion image and the reference

image The main feature of the proper IQA is that it can be

embedded in real t ime image processing system The most

advanced method to perform IQA is Structure Similarity Index

Measurement (SSIM) [51] The various features like

luminance contrast and structure are compared in the SSIM

Almost all these features are consistent with the Human

Visual System (HVS) and are compatible But there are few

drawbacks as the luminance and contrast are sensitive to the

illumination To overcome the drawbacks of the

aforementioned technique Feature Similarity Index

Measurement (FSIM) has come into existence [52] In FSIM

two features main ly Phase Congruency (PC) [53] [54] and

Gradient Magnitude (GM) are considered To compute the PC

of 2D grayscale images The 1D log-Gabor filters described

earlier can be extended to 2D ones by simply applying some

spreading function across thefilter perpendicular to its

orientation One widely used spreading functionis Gaussian

[55] [56] and [57] By using Gaussian as the spreading

function the 2D log-Gabor function has the following transfer

function

1198662 120596120579119895 = 119890119909119901 119897119900119892 120596 1205960

2

21205901199032

119890119909119901 120579minus120579119895

2

21205901205792

(14)

Where 120579119895 = 119895120587 119869 119895 = 01hellip 119869 minus 1 the orientation angle of

the filter is 119869 is the number of orientations and 120590120579determines

the filter‟s angular bandwidthBy modulat ing 120596120579 and 120579119895 and

convolving 1198662with the 2D image we get a set of responses at

each point x as 119890119899120579119895 119883 119874119899 120579119895

119883 The local amplitude on

scale n and orientation 120579119895is119860119899120579119895 119883 = 119890119899 120579119895

119883 2 +119874119899 120579119895 119883 2

and the local energy along orientation 120579119895 is119864120579119895 119883 =

119865120579119895 119883 2 + 119867120579119895

119883 2 where119865120579119895 119883 = 119890119899 120579119895

119883 119899 and

119867120579119895 119883 = 119900119899 120579119895

119883 119899 The 2D PC at x is defined as

1198751198622119863 119883 = 119864120579 119895

119883 119895

휀+ 119860119899 120579 119895 119883 119895119899

(15)

It should be noted that 1198751198622119863 119883 is a real number within 0~1

(i) The FS IM index

The computation of FSIM index consists of two stages In the

first stage the local similarity map is computed and then in

the second stage we pool the similarity map into a single

similarity score We separate the feature similarity

measurement between 1198911 119883 and 1198912 119883 into two

components each for PC or GM First the similarity measure

for 1198751198621 119883 and 1198751198622 119883 is defined as

119878119875119862 119883 =21198751198621 119883 1198751198622 119883 +1198791

11987511986212 119883 +1198751198622

2 119883 +1198791 (16)

where 1198791 is a positive constant to increase the stability of SPC

(such a consideration was also included in SSIM [51]) In practice the determination of 1198791 depends on the dynamic

range of PC values Equation 16 is a commonly used measure

to define the similarity of two positive real numbers and its

result ranges within [0 1] Similarly the GM values 1198661 119883

and 1198662 119883 are compared and the similarity measure is defined

as

119878119866 119883 =21198661 119883 1198662 119883 +1198792

11986612 119883 +1198662

2 119883 +1198792 (17)

where 1198792 is a positive constant depending on the dynamic

range of GM values In our experiments both 1198791 and 1198792 will

be fixed to all databases so that the proposed FSIM can be conveniently used Then 119878119875119862 119883 and 119878119866 119883 are combined to

get the similarity 119878119871 119883 of 1198911 119883 and 1198912 119883 We define

119878119871 119883 as

119878119871 119883 = 119878119875119862 119883 120572

119878119866 119883 120573

(18)

where 120572 and 120573 are parameters used to adjust the relative

importance of PC and GM features In this paper we set 120572 = 120573 =1 for simplicity Thus119878119871 119883 = 119878119875119862 119883 119878119866 119883 Having

obtained the similarity 119878119871 119883 at each location 119883 the overall

similarity between 1198911and 1198912 can becalculated However

different locations have different contributions to HVS‟

perception of the image For example edge locations convey

more crucial v isual information than the locations within a

smooth area Since human visual cortex is sensitive to phase

congruent structures [54] the PC value at a location canreflect

how likely it is a perceptibly significant structure point Intuitively for a given location 119883 if anyone of 1198911 119883 and

1198912 119883 has a significant PC value it implies that this position x

International Journal of Pure and Applied Mathematics Special Issue

140

will have a high impact on HVS in evaluating the similarity between 1198911 and 1198912 Therefore we use 119875119862119898 119883 =

max(1198751198621 119883 1198751198622 119883 ) to weight the importance of 119878119871 119883 in

the overall similarity between 1198911 and 1198912 and accordingly the

FSIM index between 1198911and 1198912 is defined as

119865119878119868119872 = 119878119871 119883 119883 isinΩ 119875119862119898 119883

119875119862119898 119883 119883isinΩ (19)

where Ω means the whole image spatial domain

(ii) Structural similarity index (SSIM)

The SSIM algorithm performs similarity measurement in three

steps luminance comparison contrast comparison and

structure comparison First the luminance of each image

signal is compared The estimated mean intensity is computed

as follows

120583119903119890119891 =1

119882119867 119868119903119890119891 119894 119895

119882119894 = 1

119867119895 = 1 (20)

The luminance comparison function 119897 119868119903119890119891 119868119905119904119905 is a

function of 120583119903119890119891 and 120583119905119904119905Second the contrast of each image

signal is compared For estimat ing the contrast standard

deviation is being used An unbiased estimate of standard

deviation in discrete form is as follows 120590119903119890119891

= 1

119882119867minus1 119868119903119890119891 119894 119895 minus 120583119903119890119891

2119882119894 = 1

119867119895 = 1

1

2

(21)

The contrast comparison function 119888 119868119903119890119891 119868119905119904119905 is a function

of120590119903119890119891 and 120590119905119904119905 Third the structure of each image signal is

compared Structure comparison function119904 119868119903119890119891 119868119905119904119905 is a

function of 119868119903119890119891 minus 120583119903119890119891 120590119903119890119891 and

119868119905119904119905 minus 120583119905119904119905 120590119905119904119905 Finally three comparison functions are

combined and an overall similarity measure is produced The

overall similarity measure119878 119868119903119890119891 119868119905119904119905 is a function of

119897 119868119903119890119891 119868119905119904119905 119888 119868119903119890119891 119868119905119904119905 119888 119868119903119890119891 119868119905119904119905 and 119904 119868119903119890119891 119868119905119904119905

Definitions of119897 119868119903119890119891 119868119905119904119905 119888 119868119903119890119891 119868119905119904119905 and119904 119868119903119890119891 119868119905119904119905 are as

follows

For luminance comparison function we have

119904 119868119903119890119891 119868119905119904119905 =2120583119903119890119891 120583119905119904119905 +1198791

1205831199031198901198912 +120583119905119904119905

2 +1198791 (21)

where 1198791 is a positive stabilizing constant chosen to prevent

the denominator from becoming too small We have

1198791 = 1199051119863 2 (22)

where D is the dynamic range of pixel values and 1199051 ltlt 1 is

a small constant For contrast comparison function we have

119888 119868119903119890119891 119868119905119904119905 =2120590119903119890119891 120590119905119904119905 +1198792

1205901199031198901198912 +120590119905119904119905

2 +1198792 (23)

where 1198792 = 1199052119863 2is a positive stabilizing constant

And1199052 ltlt 1 For structure comparison function we have

119904 119868119903119890119891 119868119905119904119905 =120590119903119890119891 119905119904119905+1198793

120590119903119890119891 120590119905119904119905 +1198793 (24)

where 1198793 is a positive stabilizing constant In (58)120590119903119890119891 119905119904119905 is

the correlation coefficient between the reference and test images In the discrete form120590119903119890119891 119905119904119905 can be estimated by

120590119903119890119891 119905119904119905 =1

119882119867minus1 119868119903119890119891 119894 119895 minus 120583119903119890119891 119868119905119904119905 119894 119895 minus

119882119894 = 1

119867119895 = 1

120583119905119904119905 (25)

Finally structural similarity index is defined as

119878119878119868119872 119868119903119890119891 119868119905119904119905 =

119897 119868119903119890119891 119868119905119904119905 120572 119888 119868119903119890119891 119868119905119904119905

120573 119904 119868119903119890119891 119868119905119904119905

120574 (26)

where 120572 120573 and 120574The universal quality index (UQI) [5960] is a special case of the SSIM index when1198791 = 1198792 = 1198793 = 0

and 120572 = 120573 = 120574 = 1 Since image statistical features and

distortions are usually space-variant authors of [60] employ

the SSIM index locally instead of globally Another reason for

this is that by applying the SSIM index locally a quality map

of the image which conveys more information about the

quality degradation can be generated

TABLE I SAMPLE TEN SUBJECT‟S FSIM VALUES WITH RESPECT TO EACH OTHER

Subject No

11 12 13 14 15 16 17 18 19 20

11 9342 7906 7438 7442 7648 7566 7509 78 7441 7597

12 7906 9523 734 7135 7459 745 7394 7505 7335 7449

13 7438 734 9705 743 7943 7264 776 7417 7941 7735

14 7442 7135 743 9429 8081 7252 7428 7478 7604 7406

15 7648 7459 7943 8081 943 7734 818 7903 834 8126

16 7566 745 7264 7252 7734 9247 7599 8769 7523 7713

17 7509 7394 776 7428 8189 7599 934 7552 8102 8612

18 7801 7505 7417 7478 7903 8769 7552 9342 7631 7669

19 7441 7335 7941 7604 834 7523 8102 7631 9693 806

20 7597 7449 7735 7464 8126 7713 8612 7669 806 9479

International Journal of Pure and Applied Mathematics Special Issue

141

TABLE II SAMPLE TEN SUBJECT‟S SSIM VALUES WITH RESPECT TO EACH OTHER

Subject No

11 12 13 14 15 16 17 18 19 20

11 9044 7333 6507 6937 7054 7217 6717 7433 6588 6854

12 7333 9327 6249 6298 6574 6905 6357 6976 6258 6421

13 6507 6249 9643 6744 7311 6586 7173 671 7242 7014

14 6937 6298 6744 9155 7673 6857 6911 7007 7009 6874

15 7054 6574 7311 7673 9158 7325 7676 7475 7685 7621

16 7217 6905 6586 6857 7325 925 711 867 694 7189

17 6717 6357 7173 6911 7676 711 9147 7083 7443 822

18 7433 6976 671 7007 7475 867 7083 9236 7054 7145

19 6588 6258 7242 7009 7685 694 7443 7054 9495 7423

20 6854 6421 7014 6874 7621 7189 822 7145 7423 9251

IV EXPERIMENTAL RESULTS AND ANALYSIS

In this section the performance of IQA techniques like FSIM

and SSIM are evaluated The parameters required in the

proposed methods were set as n = 4 J = 4 σr = 05978 σθ =

06545 T1 = 085 T2 = 160 T3 = T4 = 200 and λ = 003

Besides the center frequencies of the log-Gabor filters at four

scales were set as 16 112 124 and 148 These parameters

were then fixed for all the following experiments conducted

We take twenty set of database in which each database

consists of around seventy images Each and every image is

taken as the reference image and measured the similarity with

all other images present and the results are tabulated for FSIM

in Table I whereas for SSIM the results are tabulated in Table

II The average similarity index for each and every database

for the FSIM and SSIM are given in Figure 7 The results

clearly indicate that similarity measure is a good sign of a

quality measure as well as good metric to identify the

similarity between the images The results also gave a clear

indication that FSIM overcomes the drawbacks of SSIM and

gave a good measurement when compared to the SSIM

Fig 7 Graphical representation of FSIM and SSIM average values of the

given database

V CONCLUSION AND FUTURE WORK

The proposed work implemented the similarity index

assessment of thermal images following the sequence of the

work g iven as follows Darwinian Particle Swarm

Optimization is used for image segmentation as a multi-

threshold technique which has overcome various drawbacks

like computational time feature selectivity stability and

feasibility DPSO is better when compared to other

conventional multi-threshold techniques like Otsu image

segmentation fuzzy clustering PSO and ant colony

optimization Active contour image segmentation was

performed which is based on the level set based segmentation

method of Mumford Shah model producing binary image The

CORF operator extracts the contour image using Difference of

Gaussians and hysteresis thresholding The similarities of the

results are compared using FSIM and SSIM FSIM

outperforms the results of SSIM The results are good enough

to show that Image Quality Assessment techniques are helpful

in the process of identificat ion and classification of subjects

The given below points can be considered as a future work (i)

The results can be compared with other IQA metrics and (ii)

The proposed approach need to be explored in the domain of

medical imaging and satellite communicat ion

REFERENCES

[1] W Zhao R Chellappa A Rosenfeld and P Phillips ldquoFace recognition

A literature surveyrdquo ACM Computer Survey vol 35 no 4 pp 399-458 December 2003

[2] T Bourlai A Ross C Chen and L Hornak A study on using mid-wave infrared imagesfor face recognition In Proc SPIE 2012

[3] R S Ghiass O Arandjelovic A Bendada and X Maldague Infrared face recognition a literature review In Proc International Joint Conference on Neural Networks pages2791-2800 2013

[4] Yufeng Zheng ldquoFace detection and eyeglasses detection for thermal face recognitionrdquo ISampTSPIE Electronic Imaging Conference 22-26 January 2012 in Burlingame California United States

[5] F J Prokoski R B Riedel and J S Coffin ldquoIdentification of individuals by means of facial thermographyrdquo in Proceedings of The IEEE 1992 International Carnahan Conference on Security Technology Crime Countermeasures Atlanta GA USA 14-16 Oct pp 120-125 IEEE 1992

[6] Cutler R ldquoFace recognition using infrared images and eigenfacesrdquo httpciteseeristpsueducutler96facehtml April 1996 visited July 2007

[7] Socolinsky D Selinger A ldquoA comparative analysis of face recognition performance with visible and thermal infrared imageryrdquo Proceedings of the International Conference o Pattern Recognition (ICPR02) vol2 p 40217 Quebec Canada August 2002

[8] Socolinsky D Selinger A Neuheisel J ldquoFace recognition with visible and thermal infrared imageryrdquo Computer Vision amp Image Understanding vol 91 p 72-114 2003

50

60

70

80

90

100

1 3 5 7 9 11 13 15 17 19

FS

IM a

nd

SS

IM V

alu

es

Subject No

FSIM

SSIM

International Journal of Pure and Applied Mathematics Special Issue

142

[9] H-W Tzeng H-C Lee and M-Y Chen The design of isotherm face recognition technique based on nostril localization In Proc International Conference on System Science and Engineering pages 82-86 2011

[10] O Arandjelovic R I Hammoud and R Cipolla Thermal and re ectance based personal identification methodology in challenging variable illuminations Pattern Recognition 43(5)1801-1813 2010

[11] T Jin C Shouming X Xiuzhen and J Gu Eyes localization in an infrared image In Proc IEEE International Conference on Automation and Logistics (ICAL) pages 217-222 2009

[12] T Bourlai and Z Jafri Eye detection in the middle-wave infrared spectrum Towards recognition in the dark In Proc IEEE International Workshop on Information Forensic and Security (WIFS) pages 1-6 2011

[13] B Martinez X Binefa and M Pantic Facial component detection in thermal imagery In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 48-54 2010

[14] Chen X Jing Z Xiao G ldquoFuzzy fusion for face recognitionrdquo Proceedings of the International Conference on Fuzzy Systems and Knowledge Discovery (FSKD05) p 672- 675 Changsha China August 2005

[15] S Zhao and R Grigat An automatic face recognition system in the near infrared spectrum MLDM pages 437-444 2005

[16] T Elguebaly and N Bouguila ldquoA Bayesian method for infrared face recognitionrdquo Machine Vision Beyond Visible Spectrum 2011

[17] Y Yoshitomi T Miyaura S Tomita and S Kimura Face identification using thermalimage processing RO-MAN pages 374-379 1997

[18] S Li R Chu M Ao L Zhang and R He Highly accurate and fast face recognitionusing near infrared images In Proc IAPR International Conference on Biometricspages 151-158 2006

[19] H Maeng H-C Choi U Park S-W Lee and A K Jain NFRAD Near-infraredface recognition at a distance In Proc International Joint Conference on Biometrics(IJCB) pages 1-7 2011

[20] D Goswami C H Chan D Windridge and J Kittler Evaluation of face recognition system in heterogeneous environments (visible vs NIR) In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 2160-2167 2011

[21] A Srivastana and X Liu Statistical hypothesis pruning for recognizing faces from infrared images Image and Vision Computing 21(7)651-661 2003

[22] Z Xie SWu G Liu and Z Fang Infrared face recognition based on radiant energy and curvelet transformation In Proc International Conference on Information Assurance and Security (IAS) 2215-218 2009

[23] P Buddharaju I Pavlidis and P Tsiamyrtzis Pose-invariant physiological face recognition in the thermal infrared spectrum In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 53-60 2006

[24] P Buddharaju and I Pavlidis Physiological face recognition is coming of age In Proc IEEE Conference on Computer Vision and Pattern Recognition pages 128-135 2009

[25] T R Gault N Blumenthal A A Farag and T Starr Extraction of the superficial facial vasculature vital signs waveforms and rates using thermal imaging In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 1-8 2010

[26] A Seal M Nasipuri D Bhattacharjee and DK Basu Minutiae based thermal face recognition using blood perfusion data International Conference on Image Information Processing pages 1-4 2011

[27] S Cho L Wang and W J Ong Thermal imprint feature analysis for face recognitionISIE pages 1875-1880 2009

[28] R S Ghiass O Arandjelovic A Bendada and X Maldague Vesselness features and the inverse compositional AAM for robust face recognition using thermal IR In Proc AAAI Conference on Artificial Intelligence pages 357-364 2013

[29] S Wu Z Gu K A Chia and S H Ong Infrared facial recognition using modified blood perfusion ICICS pages 1-5 2007

[30] Z Xie S Wu G Liu and Z Fang Infrared face recognition method based on blood perfusion image and curvelet transformation In Proc

International Conference on Wavelet Analysis and Pattern Recognition pages 360-364 2009

[31] Kennedy J amp Eberhart R ldquoA new optimizer using particle swarm theoryrdquo in Proceedings of the IEEE sixth international symposium on micro machine andhuman science pp 39ndash43 1995

[32] Tillett J Rao T M Sahin F Rao R amp Brockport S (2005) Darwinian Particle Swarm Optimization In Proceedings of the 2nd Indian international conference onartificial intelligence (pp 1474ndash1487)

[33] Z Chenglin S Xuebin S Songlin and J Ting ldquoFault diagnosis of sensor by chaos particle swarm optimization algorithm and support vector machinerdquo Expert Systems with Applications vol 38 no 8 pp 9908ndash9912 2011

[34] P Ghamisi M S Couceiro J A Benediktsson and N M F Ferreira An Efficient Method for Segmentation of Images Based on Fractional Calculus and Natural Selection Expert Systems With Applications vol 39 no 16 pp 12407- 2417 Nov 2012

[35] P Ghamisi M S Couceiro F M L Martins and J A Benediktsson Multi-level Image Segmentation Based on Fractional-Order Darwinian Particle Swarm Optimization IEEE Transactions on Geoscience and Remote Sensing vol 52 no 5 pp 2382-2394 May 2014

[36] M S Couceiro N M F Ferreira and J A T Machado ldquoFractional order Darwinian particle swarm optimizationrdquo in proc Symp FSS Coimbra Portugal pp 4-5 Nov 2011

[37] P Ghamisi M S Couceiro and J A Benediktsson Classification of Hyperspectral Images with Binary Fractional Order Darwinian PSO and Random Forests in Proc SPIE Image and Signal Processing for Remote Sensing XIX 2013

[38] G Majumder and M K Bhowmik ldquoGabor-Fast ICA feature extraction for thermal face recognition using linear kernel support vector machinerdquo Computational Intelligence and Networks (CINE) 2015 International Conference on DOI 101109CINE201514 pp21 ndash 25 2015

[39] T Chan L Vese and Y Sandberg Active contours without edges for vector-valued images Journal of Visual Communications and Image Representation 11 no 2 (2000) pp 130-141

[40] D Mumford and J Shah Optimal approximation by piecewise smooth functions and associated variational problems Comm Pure Appl Math 42 1989 pp 577-685

[41] M Sussman P Smereka and S Osher A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow J Comput Phys V 119 (1994) pp 146-159

[42] L Vese and T Chan A multiphase level set framework for image segmentation using the mumford and shah model International Journal of Computer Vision vol 50 pp 271-293 2002

[43] T F Chan and L A Vese Image segmentation using level sets and the piecewise-constant Mumford-Shah model 2000

[44] D Cremers F R Schmidt and F Barthel Shape priors in variational image segmentation Convexity lipschitz continuity and globally optimal solutions in Computer Vision and Pattern Recognition 2008 CVPR 2008 IEEE Conference on 2008 pp 1-6

[45] S Osher and J A Sethian Fronts propagating with curvature-dependent speed algorithms based on Hamilton-Jacobi formulations Journal of computat ional physics vol 79 pp 12-49 1988

[46] R Ronfard Region-based strategies for active contour models International Journal of Computer Vision vol 13 pp 229-251 1994

[47] K Siddiqi Y B Lauziere A Tannenbaum and S W Zucker Area and length minimizing flows for shape segmentation Image Processing IEEE Transactions on vol 7 pp 433-443 1998

[48] Cosmin Grigorescu Nicolai Petkov Michel A Westenberg Contour and boundary detection improved by surround suppression of texture edges Image and Vision Computing Vol 22 pp 609-622 2004

[49] Azzopardi G Petkov N A CORF computational model of a simple cell that relies on LGN input outperforms the Gabor function model Biol Cybern 106(3) 177ndash189 (2012)

[50] Azzopardi G Petkov N Contour detection by CORF operator In Villa AEP Duch W Erdi P Masulli F Palm G (eds) ICANN 2012 Part I LNCS vol acute 7552 pp 395ndash402 Springer Heidelberg (2012)

International Journal of Pure and Applied Mathematics Special Issue

143

[51] Z Wang AC Bovik HR Sheikh and EP Simoncelli ldquoImage quality assessment from error visibility to structural similarityrdquo IEEE Trans Image Process vol 13 no 4 pp 600-612 Apr 2004

[52] Lin Zhang Lei Zhang Xuanqin Mou and David Zhang FSIM a feature similarity index for image quality assessment IEEE Transactions on Image Processing vol 20 no 8 pp 2378-2386 2011

[53] P Kovesi ldquoImage features from phase congruencyrdquo Videre J Comp Vis Res vol 1 no 3 pp 1-26 1999

[54] L Henriksson A Hyvaumlrinen and S Vanni ldquoRepresentation of cross-frequency spatial phase relationships in human visual cortexrdquo J Neuroscience vol 29 no 45 pp 14342-14351 Nov 2009

[55] C Mancas-Thillou and B Gosselin ldquoCharacter segmentation-by-recognition using log-Gabor filtersrdquo in Proc Int Conf Pattern Recognit 2006 pp 901-904

[56] S Fischer F Šroubek L Perrinet R Redondo and G Cristoacutebal ldquoSelf-invertible 2D log-Gabor waveletsrdquo Int J Computer Vision vol 75 no 2 pp 231-246 Nov 2007

[57] W Wang J Li F Huang and H Feng ldquoDesign and implementation of log-Gabor filter in fingerprint image enhancementrdquo Pattern Recognit Letters vol 29 no 3 pp 301-308 Feb 2008

[58] H R Sheikh and A C Bovik Image information and visual quality IEEE Trans Image Processing vol 15 pp 430-444 Feb 2006

[59] Z Wang Rate scalable foveated image and video communications PhD thesis Dept of ECE the University of Texas at Austin Dec 2001

[60] Z Wang and A C Bovik A universal image quality index IEEE Signal Processing Letters vol 9 pp 81-84 March 2002

International Journal of Pure and Applied Mathematics Special Issue

144

145

146

will have a high impact on HVS in evaluating the similarity between 1198911 and 1198912 Therefore we use 119875119862119898 119883 =

max(1198751198621 119883 1198751198622 119883 ) to weight the importance of 119878119871 119883 in

the overall similarity between 1198911 and 1198912 and accordingly the

FSIM index between 1198911and 1198912 is defined as

119865119878119868119872 = 119878119871 119883 119883 isinΩ 119875119862119898 119883

119875119862119898 119883 119883isinΩ (19)

where Ω means the whole image spatial domain

(ii) Structural similarity index (SSIM)

The SSIM algorithm performs similarity measurement in three

steps luminance comparison contrast comparison and

structure comparison First the luminance of each image

signal is compared The estimated mean intensity is computed

as follows

120583119903119890119891 =1

119882119867 119868119903119890119891 119894 119895

119882119894 = 1

119867119895 = 1 (20)

The luminance comparison function 119897 119868119903119890119891 119868119905119904119905 is a

function of 120583119903119890119891 and 120583119905119904119905Second the contrast of each image

signal is compared For estimat ing the contrast standard

deviation is being used An unbiased estimate of standard

deviation in discrete form is as follows 120590119903119890119891

= 1

119882119867minus1 119868119903119890119891 119894 119895 minus 120583119903119890119891

2119882119894 = 1

119867119895 = 1

1

2

(21)

The contrast comparison function 119888 119868119903119890119891 119868119905119904119905 is a function

of120590119903119890119891 and 120590119905119904119905 Third the structure of each image signal is

compared Structure comparison function119904 119868119903119890119891 119868119905119904119905 is a

function of 119868119903119890119891 minus 120583119903119890119891 120590119903119890119891 and

119868119905119904119905 minus 120583119905119904119905 120590119905119904119905 Finally three comparison functions are

combined and an overall similarity measure is produced The

overall similarity measure119878 119868119903119890119891 119868119905119904119905 is a function of

119897 119868119903119890119891 119868119905119904119905 119888 119868119903119890119891 119868119905119904119905 119888 119868119903119890119891 119868119905119904119905 and 119904 119868119903119890119891 119868119905119904119905

Definitions of119897 119868119903119890119891 119868119905119904119905 119888 119868119903119890119891 119868119905119904119905 and119904 119868119903119890119891 119868119905119904119905 are as

follows

For luminance comparison function we have

119904 119868119903119890119891 119868119905119904119905 =2120583119903119890119891 120583119905119904119905 +1198791

1205831199031198901198912 +120583119905119904119905

2 +1198791 (21)

where 1198791 is a positive stabilizing constant chosen to prevent

the denominator from becoming too small We have

1198791 = 1199051119863 2 (22)

where D is the dynamic range of pixel values and 1199051 ltlt 1 is

a small constant For contrast comparison function we have

119888 119868119903119890119891 119868119905119904119905 =2120590119903119890119891 120590119905119904119905 +1198792

1205901199031198901198912 +120590119905119904119905

2 +1198792 (23)

where 1198792 = 1199052119863 2is a positive stabilizing constant

And1199052 ltlt 1 For structure comparison function we have

119904 119868119903119890119891 119868119905119904119905 =120590119903119890119891 119905119904119905+1198793

120590119903119890119891 120590119905119904119905 +1198793 (24)

where 1198793 is a positive stabilizing constant In (58)120590119903119890119891 119905119904119905 is

the correlation coefficient between the reference and test images In the discrete form120590119903119890119891 119905119904119905 can be estimated by

120590119903119890119891 119905119904119905 =1

119882119867minus1 119868119903119890119891 119894 119895 minus 120583119903119890119891 119868119905119904119905 119894 119895 minus

119882119894 = 1

119867119895 = 1

120583119905119904119905 (25)

Finally structural similarity index is defined as

119878119878119868119872 119868119903119890119891 119868119905119904119905 =

119897 119868119903119890119891 119868119905119904119905 120572 119888 119868119903119890119891 119868119905119904119905

120573 119904 119868119903119890119891 119868119905119904119905

120574 (26)

where 120572 120573 and 120574The universal quality index (UQI) [5960] is a special case of the SSIM index when1198791 = 1198792 = 1198793 = 0

and 120572 = 120573 = 120574 = 1 Since image statistical features and

distortions are usually space-variant authors of [60] employ

the SSIM index locally instead of globally Another reason for

this is that by applying the SSIM index locally a quality map

of the image which conveys more information about the

quality degradation can be generated

TABLE I SAMPLE TEN SUBJECT‟S FSIM VALUES WITH RESPECT TO EACH OTHER

Subject No

11 12 13 14 15 16 17 18 19 20

11 9342 7906 7438 7442 7648 7566 7509 78 7441 7597

12 7906 9523 734 7135 7459 745 7394 7505 7335 7449

13 7438 734 9705 743 7943 7264 776 7417 7941 7735

14 7442 7135 743 9429 8081 7252 7428 7478 7604 7406

15 7648 7459 7943 8081 943 7734 818 7903 834 8126

16 7566 745 7264 7252 7734 9247 7599 8769 7523 7713

17 7509 7394 776 7428 8189 7599 934 7552 8102 8612

18 7801 7505 7417 7478 7903 8769 7552 9342 7631 7669

19 7441 7335 7941 7604 834 7523 8102 7631 9693 806

20 7597 7449 7735 7464 8126 7713 8612 7669 806 9479

International Journal of Pure and Applied Mathematics Special Issue

141

TABLE II SAMPLE TEN SUBJECT‟S SSIM VALUES WITH RESPECT TO EACH OTHER

Subject No

11 12 13 14 15 16 17 18 19 20

11 9044 7333 6507 6937 7054 7217 6717 7433 6588 6854

12 7333 9327 6249 6298 6574 6905 6357 6976 6258 6421

13 6507 6249 9643 6744 7311 6586 7173 671 7242 7014

14 6937 6298 6744 9155 7673 6857 6911 7007 7009 6874

15 7054 6574 7311 7673 9158 7325 7676 7475 7685 7621

16 7217 6905 6586 6857 7325 925 711 867 694 7189

17 6717 6357 7173 6911 7676 711 9147 7083 7443 822

18 7433 6976 671 7007 7475 867 7083 9236 7054 7145

19 6588 6258 7242 7009 7685 694 7443 7054 9495 7423

20 6854 6421 7014 6874 7621 7189 822 7145 7423 9251

IV EXPERIMENTAL RESULTS AND ANALYSIS

In this section the performance of IQA techniques like FSIM

and SSIM are evaluated The parameters required in the

proposed methods were set as n = 4 J = 4 σr = 05978 σθ =

06545 T1 = 085 T2 = 160 T3 = T4 = 200 and λ = 003

Besides the center frequencies of the log-Gabor filters at four

scales were set as 16 112 124 and 148 These parameters

were then fixed for all the following experiments conducted

We take twenty set of database in which each database

consists of around seventy images Each and every image is

taken as the reference image and measured the similarity with

all other images present and the results are tabulated for FSIM

in Table I whereas for SSIM the results are tabulated in Table

II The average similarity index for each and every database

for the FSIM and SSIM are given in Figure 7 The results

clearly indicate that similarity measure is a good sign of a

quality measure as well as good metric to identify the

similarity between the images The results also gave a clear

indication that FSIM overcomes the drawbacks of SSIM and

gave a good measurement when compared to the SSIM

Fig 7 Graphical representation of FSIM and SSIM average values of the

given database

V CONCLUSION AND FUTURE WORK

The proposed work implemented the similarity index

assessment of thermal images following the sequence of the

work g iven as follows Darwinian Particle Swarm

Optimization is used for image segmentation as a multi-

threshold technique which has overcome various drawbacks

like computational time feature selectivity stability and

feasibility DPSO is better when compared to other

conventional multi-threshold techniques like Otsu image

segmentation fuzzy clustering PSO and ant colony

optimization Active contour image segmentation was

performed which is based on the level set based segmentation

method of Mumford Shah model producing binary image The

CORF operator extracts the contour image using Difference of

Gaussians and hysteresis thresholding The similarities of the

results are compared using FSIM and SSIM FSIM

outperforms the results of SSIM The results are good enough

to show that Image Quality Assessment techniques are helpful

in the process of identificat ion and classification of subjects

The given below points can be considered as a future work (i)

The results can be compared with other IQA metrics and (ii)

The proposed approach need to be explored in the domain of

medical imaging and satellite communicat ion

REFERENCES

[1] W Zhao R Chellappa A Rosenfeld and P Phillips ldquoFace recognition

A literature surveyrdquo ACM Computer Survey vol 35 no 4 pp 399-458 December 2003

[2] T Bourlai A Ross C Chen and L Hornak A study on using mid-wave infrared imagesfor face recognition In Proc SPIE 2012

[3] R S Ghiass O Arandjelovic A Bendada and X Maldague Infrared face recognition a literature review In Proc International Joint Conference on Neural Networks pages2791-2800 2013

[4] Yufeng Zheng ldquoFace detection and eyeglasses detection for thermal face recognitionrdquo ISampTSPIE Electronic Imaging Conference 22-26 January 2012 in Burlingame California United States

[5] F J Prokoski R B Riedel and J S Coffin ldquoIdentification of individuals by means of facial thermographyrdquo in Proceedings of The IEEE 1992 International Carnahan Conference on Security Technology Crime Countermeasures Atlanta GA USA 14-16 Oct pp 120-125 IEEE 1992

[6] Cutler R ldquoFace recognition using infrared images and eigenfacesrdquo httpciteseeristpsueducutler96facehtml April 1996 visited July 2007

[7] Socolinsky D Selinger A ldquoA comparative analysis of face recognition performance with visible and thermal infrared imageryrdquo Proceedings of the International Conference o Pattern Recognition (ICPR02) vol2 p 40217 Quebec Canada August 2002

[8] Socolinsky D Selinger A Neuheisel J ldquoFace recognition with visible and thermal infrared imageryrdquo Computer Vision amp Image Understanding vol 91 p 72-114 2003

50

60

70

80

90

100

1 3 5 7 9 11 13 15 17 19

FS

IM a

nd

SS

IM V

alu

es

Subject No

FSIM

SSIM

International Journal of Pure and Applied Mathematics Special Issue

142

[9] H-W Tzeng H-C Lee and M-Y Chen The design of isotherm face recognition technique based on nostril localization In Proc International Conference on System Science and Engineering pages 82-86 2011

[10] O Arandjelovic R I Hammoud and R Cipolla Thermal and re ectance based personal identification methodology in challenging variable illuminations Pattern Recognition 43(5)1801-1813 2010

[11] T Jin C Shouming X Xiuzhen and J Gu Eyes localization in an infrared image In Proc IEEE International Conference on Automation and Logistics (ICAL) pages 217-222 2009

[12] T Bourlai and Z Jafri Eye detection in the middle-wave infrared spectrum Towards recognition in the dark In Proc IEEE International Workshop on Information Forensic and Security (WIFS) pages 1-6 2011

[13] B Martinez X Binefa and M Pantic Facial component detection in thermal imagery In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 48-54 2010

[14] Chen X Jing Z Xiao G ldquoFuzzy fusion for face recognitionrdquo Proceedings of the International Conference on Fuzzy Systems and Knowledge Discovery (FSKD05) p 672- 675 Changsha China August 2005

[15] S Zhao and R Grigat An automatic face recognition system in the near infrared spectrum MLDM pages 437-444 2005

[16] T Elguebaly and N Bouguila ldquoA Bayesian method for infrared face recognitionrdquo Machine Vision Beyond Visible Spectrum 2011

[17] Y Yoshitomi T Miyaura S Tomita and S Kimura Face identification using thermalimage processing RO-MAN pages 374-379 1997

[18] S Li R Chu M Ao L Zhang and R He Highly accurate and fast face recognitionusing near infrared images In Proc IAPR International Conference on Biometricspages 151-158 2006

[19] H Maeng H-C Choi U Park S-W Lee and A K Jain NFRAD Near-infraredface recognition at a distance In Proc International Joint Conference on Biometrics(IJCB) pages 1-7 2011

[20] D Goswami C H Chan D Windridge and J Kittler Evaluation of face recognition system in heterogeneous environments (visible vs NIR) In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 2160-2167 2011

[21] A Srivastana and X Liu Statistical hypothesis pruning for recognizing faces from infrared images Image and Vision Computing 21(7)651-661 2003

[22] Z Xie SWu G Liu and Z Fang Infrared face recognition based on radiant energy and curvelet transformation In Proc International Conference on Information Assurance and Security (IAS) 2215-218 2009

[23] P Buddharaju I Pavlidis and P Tsiamyrtzis Pose-invariant physiological face recognition in the thermal infrared spectrum In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 53-60 2006

[24] P Buddharaju and I Pavlidis Physiological face recognition is coming of age In Proc IEEE Conference on Computer Vision and Pattern Recognition pages 128-135 2009

[25] T R Gault N Blumenthal A A Farag and T Starr Extraction of the superficial facial vasculature vital signs waveforms and rates using thermal imaging In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 1-8 2010

[26] A Seal M Nasipuri D Bhattacharjee and DK Basu Minutiae based thermal face recognition using blood perfusion data International Conference on Image Information Processing pages 1-4 2011

[27] S Cho L Wang and W J Ong Thermal imprint feature analysis for face recognitionISIE pages 1875-1880 2009

[28] R S Ghiass O Arandjelovic A Bendada and X Maldague Vesselness features and the inverse compositional AAM for robust face recognition using thermal IR In Proc AAAI Conference on Artificial Intelligence pages 357-364 2013

[29] S Wu Z Gu K A Chia and S H Ong Infrared facial recognition using modified blood perfusion ICICS pages 1-5 2007

[30] Z Xie S Wu G Liu and Z Fang Infrared face recognition method based on blood perfusion image and curvelet transformation In Proc

International Conference on Wavelet Analysis and Pattern Recognition pages 360-364 2009

[31] Kennedy J amp Eberhart R ldquoA new optimizer using particle swarm theoryrdquo in Proceedings of the IEEE sixth international symposium on micro machine andhuman science pp 39ndash43 1995

[32] Tillett J Rao T M Sahin F Rao R amp Brockport S (2005) Darwinian Particle Swarm Optimization In Proceedings of the 2nd Indian international conference onartificial intelligence (pp 1474ndash1487)

[33] Z Chenglin S Xuebin S Songlin and J Ting ldquoFault diagnosis of sensor by chaos particle swarm optimization algorithm and support vector machinerdquo Expert Systems with Applications vol 38 no 8 pp 9908ndash9912 2011

[34] P Ghamisi M S Couceiro J A Benediktsson and N M F Ferreira An Efficient Method for Segmentation of Images Based on Fractional Calculus and Natural Selection Expert Systems With Applications vol 39 no 16 pp 12407- 2417 Nov 2012

[35] P Ghamisi M S Couceiro F M L Martins and J A Benediktsson Multi-level Image Segmentation Based on Fractional-Order Darwinian Particle Swarm Optimization IEEE Transactions on Geoscience and Remote Sensing vol 52 no 5 pp 2382-2394 May 2014

[36] M S Couceiro N M F Ferreira and J A T Machado ldquoFractional order Darwinian particle swarm optimizationrdquo in proc Symp FSS Coimbra Portugal pp 4-5 Nov 2011

[37] P Ghamisi M S Couceiro and J A Benediktsson Classification of Hyperspectral Images with Binary Fractional Order Darwinian PSO and Random Forests in Proc SPIE Image and Signal Processing for Remote Sensing XIX 2013

[38] G Majumder and M K Bhowmik ldquoGabor-Fast ICA feature extraction for thermal face recognition using linear kernel support vector machinerdquo Computational Intelligence and Networks (CINE) 2015 International Conference on DOI 101109CINE201514 pp21 ndash 25 2015

[39] T Chan L Vese and Y Sandberg Active contours without edges for vector-valued images Journal of Visual Communications and Image Representation 11 no 2 (2000) pp 130-141

[40] D Mumford and J Shah Optimal approximation by piecewise smooth functions and associated variational problems Comm Pure Appl Math 42 1989 pp 577-685

[41] M Sussman P Smereka and S Osher A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow J Comput Phys V 119 (1994) pp 146-159

[42] L Vese and T Chan A multiphase level set framework for image segmentation using the mumford and shah model International Journal of Computer Vision vol 50 pp 271-293 2002

[43] T F Chan and L A Vese Image segmentation using level sets and the piecewise-constant Mumford-Shah model 2000

[44] D Cremers F R Schmidt and F Barthel Shape priors in variational image segmentation Convexity lipschitz continuity and globally optimal solutions in Computer Vision and Pattern Recognition 2008 CVPR 2008 IEEE Conference on 2008 pp 1-6

[45] S Osher and J A Sethian Fronts propagating with curvature-dependent speed algorithms based on Hamilton-Jacobi formulations Journal of computat ional physics vol 79 pp 12-49 1988

[46] R Ronfard Region-based strategies for active contour models International Journal of Computer Vision vol 13 pp 229-251 1994

[47] K Siddiqi Y B Lauziere A Tannenbaum and S W Zucker Area and length minimizing flows for shape segmentation Image Processing IEEE Transactions on vol 7 pp 433-443 1998

[48] Cosmin Grigorescu Nicolai Petkov Michel A Westenberg Contour and boundary detection improved by surround suppression of texture edges Image and Vision Computing Vol 22 pp 609-622 2004

[49] Azzopardi G Petkov N A CORF computational model of a simple cell that relies on LGN input outperforms the Gabor function model Biol Cybern 106(3) 177ndash189 (2012)

[50] Azzopardi G Petkov N Contour detection by CORF operator In Villa AEP Duch W Erdi P Masulli F Palm G (eds) ICANN 2012 Part I LNCS vol acute 7552 pp 395ndash402 Springer Heidelberg (2012)

International Journal of Pure and Applied Mathematics Special Issue

143

[51] Z Wang AC Bovik HR Sheikh and EP Simoncelli ldquoImage quality assessment from error visibility to structural similarityrdquo IEEE Trans Image Process vol 13 no 4 pp 600-612 Apr 2004

[52] Lin Zhang Lei Zhang Xuanqin Mou and David Zhang FSIM a feature similarity index for image quality assessment IEEE Transactions on Image Processing vol 20 no 8 pp 2378-2386 2011

[53] P Kovesi ldquoImage features from phase congruencyrdquo Videre J Comp Vis Res vol 1 no 3 pp 1-26 1999

[54] L Henriksson A Hyvaumlrinen and S Vanni ldquoRepresentation of cross-frequency spatial phase relationships in human visual cortexrdquo J Neuroscience vol 29 no 45 pp 14342-14351 Nov 2009

[55] C Mancas-Thillou and B Gosselin ldquoCharacter segmentation-by-recognition using log-Gabor filtersrdquo in Proc Int Conf Pattern Recognit 2006 pp 901-904

[56] S Fischer F Šroubek L Perrinet R Redondo and G Cristoacutebal ldquoSelf-invertible 2D log-Gabor waveletsrdquo Int J Computer Vision vol 75 no 2 pp 231-246 Nov 2007

[57] W Wang J Li F Huang and H Feng ldquoDesign and implementation of log-Gabor filter in fingerprint image enhancementrdquo Pattern Recognit Letters vol 29 no 3 pp 301-308 Feb 2008

[58] H R Sheikh and A C Bovik Image information and visual quality IEEE Trans Image Processing vol 15 pp 430-444 Feb 2006

[59] Z Wang Rate scalable foveated image and video communications PhD thesis Dept of ECE the University of Texas at Austin Dec 2001

[60] Z Wang and A C Bovik A universal image quality index IEEE Signal Processing Letters vol 9 pp 81-84 March 2002

International Journal of Pure and Applied Mathematics Special Issue

144

145

146

TABLE II SAMPLE TEN SUBJECT‟S SSIM VALUES WITH RESPECT TO EACH OTHER

Subject No

11 12 13 14 15 16 17 18 19 20

11 9044 7333 6507 6937 7054 7217 6717 7433 6588 6854

12 7333 9327 6249 6298 6574 6905 6357 6976 6258 6421

13 6507 6249 9643 6744 7311 6586 7173 671 7242 7014

14 6937 6298 6744 9155 7673 6857 6911 7007 7009 6874

15 7054 6574 7311 7673 9158 7325 7676 7475 7685 7621

16 7217 6905 6586 6857 7325 925 711 867 694 7189

17 6717 6357 7173 6911 7676 711 9147 7083 7443 822

18 7433 6976 671 7007 7475 867 7083 9236 7054 7145

19 6588 6258 7242 7009 7685 694 7443 7054 9495 7423

20 6854 6421 7014 6874 7621 7189 822 7145 7423 9251

IV EXPERIMENTAL RESULTS AND ANALYSIS

In this section the performance of IQA techniques like FSIM

and SSIM are evaluated The parameters required in the

proposed methods were set as n = 4 J = 4 σr = 05978 σθ =

06545 T1 = 085 T2 = 160 T3 = T4 = 200 and λ = 003

Besides the center frequencies of the log-Gabor filters at four

scales were set as 16 112 124 and 148 These parameters

were then fixed for all the following experiments conducted

We take twenty set of database in which each database

consists of around seventy images Each and every image is

taken as the reference image and measured the similarity with

all other images present and the results are tabulated for FSIM

in Table I whereas for SSIM the results are tabulated in Table

II The average similarity index for each and every database

for the FSIM and SSIM are given in Figure 7 The results

clearly indicate that similarity measure is a good sign of a

quality measure as well as good metric to identify the

similarity between the images The results also gave a clear

indication that FSIM overcomes the drawbacks of SSIM and

gave a good measurement when compared to the SSIM

Fig 7 Graphical representation of FSIM and SSIM average values of the

given database

V CONCLUSION AND FUTURE WORK

The proposed work implemented the similarity index

assessment of thermal images following the sequence of the

work g iven as follows Darwinian Particle Swarm

Optimization is used for image segmentation as a multi-

threshold technique which has overcome various drawbacks

like computational time feature selectivity stability and

feasibility DPSO is better when compared to other

conventional multi-threshold techniques like Otsu image

segmentation fuzzy clustering PSO and ant colony

optimization Active contour image segmentation was

performed which is based on the level set based segmentation

method of Mumford Shah model producing binary image The

CORF operator extracts the contour image using Difference of

Gaussians and hysteresis thresholding The similarities of the

results are compared using FSIM and SSIM FSIM

outperforms the results of SSIM The results are good enough

to show that Image Quality Assessment techniques are helpful

in the process of identificat ion and classification of subjects

The given below points can be considered as a future work (i)

The results can be compared with other IQA metrics and (ii)

The proposed approach need to be explored in the domain of

medical imaging and satellite communicat ion

REFERENCES

[1] W Zhao R Chellappa A Rosenfeld and P Phillips ldquoFace recognition

A literature surveyrdquo ACM Computer Survey vol 35 no 4 pp 399-458 December 2003

[2] T Bourlai A Ross C Chen and L Hornak A study on using mid-wave infrared imagesfor face recognition In Proc SPIE 2012

[3] R S Ghiass O Arandjelovic A Bendada and X Maldague Infrared face recognition a literature review In Proc International Joint Conference on Neural Networks pages2791-2800 2013

[4] Yufeng Zheng ldquoFace detection and eyeglasses detection for thermal face recognitionrdquo ISampTSPIE Electronic Imaging Conference 22-26 January 2012 in Burlingame California United States

[5] F J Prokoski R B Riedel and J S Coffin ldquoIdentification of individuals by means of facial thermographyrdquo in Proceedings of The IEEE 1992 International Carnahan Conference on Security Technology Crime Countermeasures Atlanta GA USA 14-16 Oct pp 120-125 IEEE 1992

[6] Cutler R ldquoFace recognition using infrared images and eigenfacesrdquo httpciteseeristpsueducutler96facehtml April 1996 visited July 2007

[7] Socolinsky D Selinger A ldquoA comparative analysis of face recognition performance with visible and thermal infrared imageryrdquo Proceedings of the International Conference o Pattern Recognition (ICPR02) vol2 p 40217 Quebec Canada August 2002

[8] Socolinsky D Selinger A Neuheisel J ldquoFace recognition with visible and thermal infrared imageryrdquo Computer Vision amp Image Understanding vol 91 p 72-114 2003

50

60

70

80

90

100

1 3 5 7 9 11 13 15 17 19

FS

IM a

nd

SS

IM V

alu

es

Subject No

FSIM

SSIM

International Journal of Pure and Applied Mathematics Special Issue

142

[9] H-W Tzeng H-C Lee and M-Y Chen The design of isotherm face recognition technique based on nostril localization In Proc International Conference on System Science and Engineering pages 82-86 2011

[10] O Arandjelovic R I Hammoud and R Cipolla Thermal and re ectance based personal identification methodology in challenging variable illuminations Pattern Recognition 43(5)1801-1813 2010

[11] T Jin C Shouming X Xiuzhen and J Gu Eyes localization in an infrared image In Proc IEEE International Conference on Automation and Logistics (ICAL) pages 217-222 2009

[12] T Bourlai and Z Jafri Eye detection in the middle-wave infrared spectrum Towards recognition in the dark In Proc IEEE International Workshop on Information Forensic and Security (WIFS) pages 1-6 2011

[13] B Martinez X Binefa and M Pantic Facial component detection in thermal imagery In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 48-54 2010

[14] Chen X Jing Z Xiao G ldquoFuzzy fusion for face recognitionrdquo Proceedings of the International Conference on Fuzzy Systems and Knowledge Discovery (FSKD05) p 672- 675 Changsha China August 2005

[15] S Zhao and R Grigat An automatic face recognition system in the near infrared spectrum MLDM pages 437-444 2005

[16] T Elguebaly and N Bouguila ldquoA Bayesian method for infrared face recognitionrdquo Machine Vision Beyond Visible Spectrum 2011

[17] Y Yoshitomi T Miyaura S Tomita and S Kimura Face identification using thermalimage processing RO-MAN pages 374-379 1997

[18] S Li R Chu M Ao L Zhang and R He Highly accurate and fast face recognitionusing near infrared images In Proc IAPR International Conference on Biometricspages 151-158 2006

[19] H Maeng H-C Choi U Park S-W Lee and A K Jain NFRAD Near-infraredface recognition at a distance In Proc International Joint Conference on Biometrics(IJCB) pages 1-7 2011

[20] D Goswami C H Chan D Windridge and J Kittler Evaluation of face recognition system in heterogeneous environments (visible vs NIR) In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 2160-2167 2011

[21] A Srivastana and X Liu Statistical hypothesis pruning for recognizing faces from infrared images Image and Vision Computing 21(7)651-661 2003

[22] Z Xie SWu G Liu and Z Fang Infrared face recognition based on radiant energy and curvelet transformation In Proc International Conference on Information Assurance and Security (IAS) 2215-218 2009

[23] P Buddharaju I Pavlidis and P Tsiamyrtzis Pose-invariant physiological face recognition in the thermal infrared spectrum In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 53-60 2006

[24] P Buddharaju and I Pavlidis Physiological face recognition is coming of age In Proc IEEE Conference on Computer Vision and Pattern Recognition pages 128-135 2009

[25] T R Gault N Blumenthal A A Farag and T Starr Extraction of the superficial facial vasculature vital signs waveforms and rates using thermal imaging In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 1-8 2010

[26] A Seal M Nasipuri D Bhattacharjee and DK Basu Minutiae based thermal face recognition using blood perfusion data International Conference on Image Information Processing pages 1-4 2011

[27] S Cho L Wang and W J Ong Thermal imprint feature analysis for face recognitionISIE pages 1875-1880 2009

[28] R S Ghiass O Arandjelovic A Bendada and X Maldague Vesselness features and the inverse compositional AAM for robust face recognition using thermal IR In Proc AAAI Conference on Artificial Intelligence pages 357-364 2013

[29] S Wu Z Gu K A Chia and S H Ong Infrared facial recognition using modified blood perfusion ICICS pages 1-5 2007

[30] Z Xie S Wu G Liu and Z Fang Infrared face recognition method based on blood perfusion image and curvelet transformation In Proc

International Conference on Wavelet Analysis and Pattern Recognition pages 360-364 2009

[31] Kennedy J amp Eberhart R ldquoA new optimizer using particle swarm theoryrdquo in Proceedings of the IEEE sixth international symposium on micro machine andhuman science pp 39ndash43 1995

[32] Tillett J Rao T M Sahin F Rao R amp Brockport S (2005) Darwinian Particle Swarm Optimization In Proceedings of the 2nd Indian international conference onartificial intelligence (pp 1474ndash1487)

[33] Z Chenglin S Xuebin S Songlin and J Ting ldquoFault diagnosis of sensor by chaos particle swarm optimization algorithm and support vector machinerdquo Expert Systems with Applications vol 38 no 8 pp 9908ndash9912 2011

[34] P Ghamisi M S Couceiro J A Benediktsson and N M F Ferreira An Efficient Method for Segmentation of Images Based on Fractional Calculus and Natural Selection Expert Systems With Applications vol 39 no 16 pp 12407- 2417 Nov 2012

[35] P Ghamisi M S Couceiro F M L Martins and J A Benediktsson Multi-level Image Segmentation Based on Fractional-Order Darwinian Particle Swarm Optimization IEEE Transactions on Geoscience and Remote Sensing vol 52 no 5 pp 2382-2394 May 2014

[36] M S Couceiro N M F Ferreira and J A T Machado ldquoFractional order Darwinian particle swarm optimizationrdquo in proc Symp FSS Coimbra Portugal pp 4-5 Nov 2011

[37] P Ghamisi M S Couceiro and J A Benediktsson Classification of Hyperspectral Images with Binary Fractional Order Darwinian PSO and Random Forests in Proc SPIE Image and Signal Processing for Remote Sensing XIX 2013

[38] G Majumder and M K Bhowmik ldquoGabor-Fast ICA feature extraction for thermal face recognition using linear kernel support vector machinerdquo Computational Intelligence and Networks (CINE) 2015 International Conference on DOI 101109CINE201514 pp21 ndash 25 2015

[39] T Chan L Vese and Y Sandberg Active contours without edges for vector-valued images Journal of Visual Communications and Image Representation 11 no 2 (2000) pp 130-141

[40] D Mumford and J Shah Optimal approximation by piecewise smooth functions and associated variational problems Comm Pure Appl Math 42 1989 pp 577-685

[41] M Sussman P Smereka and S Osher A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow J Comput Phys V 119 (1994) pp 146-159

[42] L Vese and T Chan A multiphase level set framework for image segmentation using the mumford and shah model International Journal of Computer Vision vol 50 pp 271-293 2002

[43] T F Chan and L A Vese Image segmentation using level sets and the piecewise-constant Mumford-Shah model 2000

[44] D Cremers F R Schmidt and F Barthel Shape priors in variational image segmentation Convexity lipschitz continuity and globally optimal solutions in Computer Vision and Pattern Recognition 2008 CVPR 2008 IEEE Conference on 2008 pp 1-6

[45] S Osher and J A Sethian Fronts propagating with curvature-dependent speed algorithms based on Hamilton-Jacobi formulations Journal of computat ional physics vol 79 pp 12-49 1988

[46] R Ronfard Region-based strategies for active contour models International Journal of Computer Vision vol 13 pp 229-251 1994

[47] K Siddiqi Y B Lauziere A Tannenbaum and S W Zucker Area and length minimizing flows for shape segmentation Image Processing IEEE Transactions on vol 7 pp 433-443 1998

[48] Cosmin Grigorescu Nicolai Petkov Michel A Westenberg Contour and boundary detection improved by surround suppression of texture edges Image and Vision Computing Vol 22 pp 609-622 2004

[49] Azzopardi G Petkov N A CORF computational model of a simple cell that relies on LGN input outperforms the Gabor function model Biol Cybern 106(3) 177ndash189 (2012)

[50] Azzopardi G Petkov N Contour detection by CORF operator In Villa AEP Duch W Erdi P Masulli F Palm G (eds) ICANN 2012 Part I LNCS vol acute 7552 pp 395ndash402 Springer Heidelberg (2012)

International Journal of Pure and Applied Mathematics Special Issue

143

[51] Z Wang AC Bovik HR Sheikh and EP Simoncelli ldquoImage quality assessment from error visibility to structural similarityrdquo IEEE Trans Image Process vol 13 no 4 pp 600-612 Apr 2004

[52] Lin Zhang Lei Zhang Xuanqin Mou and David Zhang FSIM a feature similarity index for image quality assessment IEEE Transactions on Image Processing vol 20 no 8 pp 2378-2386 2011

[53] P Kovesi ldquoImage features from phase congruencyrdquo Videre J Comp Vis Res vol 1 no 3 pp 1-26 1999

[54] L Henriksson A Hyvaumlrinen and S Vanni ldquoRepresentation of cross-frequency spatial phase relationships in human visual cortexrdquo J Neuroscience vol 29 no 45 pp 14342-14351 Nov 2009

[55] C Mancas-Thillou and B Gosselin ldquoCharacter segmentation-by-recognition using log-Gabor filtersrdquo in Proc Int Conf Pattern Recognit 2006 pp 901-904

[56] S Fischer F Šroubek L Perrinet R Redondo and G Cristoacutebal ldquoSelf-invertible 2D log-Gabor waveletsrdquo Int J Computer Vision vol 75 no 2 pp 231-246 Nov 2007

[57] W Wang J Li F Huang and H Feng ldquoDesign and implementation of log-Gabor filter in fingerprint image enhancementrdquo Pattern Recognit Letters vol 29 no 3 pp 301-308 Feb 2008

[58] H R Sheikh and A C Bovik Image information and visual quality IEEE Trans Image Processing vol 15 pp 430-444 Feb 2006

[59] Z Wang Rate scalable foveated image and video communications PhD thesis Dept of ECE the University of Texas at Austin Dec 2001

[60] Z Wang and A C Bovik A universal image quality index IEEE Signal Processing Letters vol 9 pp 81-84 March 2002

International Journal of Pure and Applied Mathematics Special Issue

144

145

146

[9] H-W Tzeng H-C Lee and M-Y Chen The design of isotherm face recognition technique based on nostril localization In Proc International Conference on System Science and Engineering pages 82-86 2011

[10] O Arandjelovic R I Hammoud and R Cipolla Thermal and re ectance based personal identification methodology in challenging variable illuminations Pattern Recognition 43(5)1801-1813 2010

[11] T Jin C Shouming X Xiuzhen and J Gu Eyes localization in an infrared image In Proc IEEE International Conference on Automation and Logistics (ICAL) pages 217-222 2009

[12] T Bourlai and Z Jafri Eye detection in the middle-wave infrared spectrum Towards recognition in the dark In Proc IEEE International Workshop on Information Forensic and Security (WIFS) pages 1-6 2011

[13] B Martinez X Binefa and M Pantic Facial component detection in thermal imagery In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 48-54 2010

[14] Chen X Jing Z Xiao G ldquoFuzzy fusion for face recognitionrdquo Proceedings of the International Conference on Fuzzy Systems and Knowledge Discovery (FSKD05) p 672- 675 Changsha China August 2005

[15] S Zhao and R Grigat An automatic face recognition system in the near infrared spectrum MLDM pages 437-444 2005

[16] T Elguebaly and N Bouguila ldquoA Bayesian method for infrared face recognitionrdquo Machine Vision Beyond Visible Spectrum 2011

[17] Y Yoshitomi T Miyaura S Tomita and S Kimura Face identification using thermalimage processing RO-MAN pages 374-379 1997

[18] S Li R Chu M Ao L Zhang and R He Highly accurate and fast face recognitionusing near infrared images In Proc IAPR International Conference on Biometricspages 151-158 2006

[19] H Maeng H-C Choi U Park S-W Lee and A K Jain NFRAD Near-infraredface recognition at a distance In Proc International Joint Conference on Biometrics(IJCB) pages 1-7 2011

[20] D Goswami C H Chan D Windridge and J Kittler Evaluation of face recognition system in heterogeneous environments (visible vs NIR) In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 2160-2167 2011

[21] A Srivastana and X Liu Statistical hypothesis pruning for recognizing faces from infrared images Image and Vision Computing 21(7)651-661 2003

[22] Z Xie SWu G Liu and Z Fang Infrared face recognition based on radiant energy and curvelet transformation In Proc International Conference on Information Assurance and Security (IAS) 2215-218 2009

[23] P Buddharaju I Pavlidis and P Tsiamyrtzis Pose-invariant physiological face recognition in the thermal infrared spectrum In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 53-60 2006

[24] P Buddharaju and I Pavlidis Physiological face recognition is coming of age In Proc IEEE Conference on Computer Vision and Pattern Recognition pages 128-135 2009

[25] T R Gault N Blumenthal A A Farag and T Starr Extraction of the superficial facial vasculature vital signs waveforms and rates using thermal imaging In Proc IEEE Conference on Computer Vision and Pattern Recognition Workshops pages 1-8 2010

[26] A Seal M Nasipuri D Bhattacharjee and DK Basu Minutiae based thermal face recognition using blood perfusion data International Conference on Image Information Processing pages 1-4 2011

[27] S Cho L Wang and W J Ong Thermal imprint feature analysis for face recognitionISIE pages 1875-1880 2009

[28] R S Ghiass O Arandjelovic A Bendada and X Maldague Vesselness features and the inverse compositional AAM for robust face recognition using thermal IR In Proc AAAI Conference on Artificial Intelligence pages 357-364 2013

[29] S Wu Z Gu K A Chia and S H Ong Infrared facial recognition using modified blood perfusion ICICS pages 1-5 2007

[30] Z Xie S Wu G Liu and Z Fang Infrared face recognition method based on blood perfusion image and curvelet transformation In Proc

International Conference on Wavelet Analysis and Pattern Recognition pages 360-364 2009

[31] Kennedy J amp Eberhart R ldquoA new optimizer using particle swarm theoryrdquo in Proceedings of the IEEE sixth international symposium on micro machine andhuman science pp 39ndash43 1995

[32] Tillett J Rao T M Sahin F Rao R amp Brockport S (2005) Darwinian Particle Swarm Optimization In Proceedings of the 2nd Indian international conference onartificial intelligence (pp 1474ndash1487)

[33] Z Chenglin S Xuebin S Songlin and J Ting ldquoFault diagnosis of sensor by chaos particle swarm optimization algorithm and support vector machinerdquo Expert Systems with Applications vol 38 no 8 pp 9908ndash9912 2011

[34] P Ghamisi M S Couceiro J A Benediktsson and N M F Ferreira An Efficient Method for Segmentation of Images Based on Fractional Calculus and Natural Selection Expert Systems With Applications vol 39 no 16 pp 12407- 2417 Nov 2012

[35] P Ghamisi M S Couceiro F M L Martins and J A Benediktsson Multi-level Image Segmentation Based on Fractional-Order Darwinian Particle Swarm Optimization IEEE Transactions on Geoscience and Remote Sensing vol 52 no 5 pp 2382-2394 May 2014

[36] M S Couceiro N M F Ferreira and J A T Machado ldquoFractional order Darwinian particle swarm optimizationrdquo in proc Symp FSS Coimbra Portugal pp 4-5 Nov 2011

[37] P Ghamisi M S Couceiro and J A Benediktsson Classification of Hyperspectral Images with Binary Fractional Order Darwinian PSO and Random Forests in Proc SPIE Image and Signal Processing for Remote Sensing XIX 2013

[38] G Majumder and M K Bhowmik ldquoGabor-Fast ICA feature extraction for thermal face recognition using linear kernel support vector machinerdquo Computational Intelligence and Networks (CINE) 2015 International Conference on DOI 101109CINE201514 pp21 ndash 25 2015

[39] T Chan L Vese and Y Sandberg Active contours without edges for vector-valued images Journal of Visual Communications and Image Representation 11 no 2 (2000) pp 130-141

[40] D Mumford and J Shah Optimal approximation by piecewise smooth functions and associated variational problems Comm Pure Appl Math 42 1989 pp 577-685

[41] M Sussman P Smereka and S Osher A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow J Comput Phys V 119 (1994) pp 146-159

[42] L Vese and T Chan A multiphase level set framework for image segmentation using the mumford and shah model International Journal of Computer Vision vol 50 pp 271-293 2002

[43] T F Chan and L A Vese Image segmentation using level sets and the piecewise-constant Mumford-Shah model 2000

[44] D Cremers F R Schmidt and F Barthel Shape priors in variational image segmentation Convexity lipschitz continuity and globally optimal solutions in Computer Vision and Pattern Recognition 2008 CVPR 2008 IEEE Conference on 2008 pp 1-6

[45] S Osher and J A Sethian Fronts propagating with curvature-dependent speed algorithms based on Hamilton-Jacobi formulations Journal of computat ional physics vol 79 pp 12-49 1988

[46] R Ronfard Region-based strategies for active contour models International Journal of Computer Vision vol 13 pp 229-251 1994

[47] K Siddiqi Y B Lauziere A Tannenbaum and S W Zucker Area and length minimizing flows for shape segmentation Image Processing IEEE Transactions on vol 7 pp 433-443 1998

[48] Cosmin Grigorescu Nicolai Petkov Michel A Westenberg Contour and boundary detection improved by surround suppression of texture edges Image and Vision Computing Vol 22 pp 609-622 2004

[49] Azzopardi G Petkov N A CORF computational model of a simple cell that relies on LGN input outperforms the Gabor function model Biol Cybern 106(3) 177ndash189 (2012)

[50] Azzopardi G Petkov N Contour detection by CORF operator In Villa AEP Duch W Erdi P Masulli F Palm G (eds) ICANN 2012 Part I LNCS vol acute 7552 pp 395ndash402 Springer Heidelberg (2012)

International Journal of Pure and Applied Mathematics Special Issue

143

[51] Z Wang AC Bovik HR Sheikh and EP Simoncelli ldquoImage quality assessment from error visibility to structural similarityrdquo IEEE Trans Image Process vol 13 no 4 pp 600-612 Apr 2004

[52] Lin Zhang Lei Zhang Xuanqin Mou and David Zhang FSIM a feature similarity index for image quality assessment IEEE Transactions on Image Processing vol 20 no 8 pp 2378-2386 2011

[53] P Kovesi ldquoImage features from phase congruencyrdquo Videre J Comp Vis Res vol 1 no 3 pp 1-26 1999

[54] L Henriksson A Hyvaumlrinen and S Vanni ldquoRepresentation of cross-frequency spatial phase relationships in human visual cortexrdquo J Neuroscience vol 29 no 45 pp 14342-14351 Nov 2009

[55] C Mancas-Thillou and B Gosselin ldquoCharacter segmentation-by-recognition using log-Gabor filtersrdquo in Proc Int Conf Pattern Recognit 2006 pp 901-904

[56] S Fischer F Šroubek L Perrinet R Redondo and G Cristoacutebal ldquoSelf-invertible 2D log-Gabor waveletsrdquo Int J Computer Vision vol 75 no 2 pp 231-246 Nov 2007

[57] W Wang J Li F Huang and H Feng ldquoDesign and implementation of log-Gabor filter in fingerprint image enhancementrdquo Pattern Recognit Letters vol 29 no 3 pp 301-308 Feb 2008

[58] H R Sheikh and A C Bovik Image information and visual quality IEEE Trans Image Processing vol 15 pp 430-444 Feb 2006

[59] Z Wang Rate scalable foveated image and video communications PhD thesis Dept of ECE the University of Texas at Austin Dec 2001

[60] Z Wang and A C Bovik A universal image quality index IEEE Signal Processing Letters vol 9 pp 81-84 March 2002

International Journal of Pure and Applied Mathematics Special Issue

144

145

146

[51] Z Wang AC Bovik HR Sheikh and EP Simoncelli ldquoImage quality assessment from error visibility to structural similarityrdquo IEEE Trans Image Process vol 13 no 4 pp 600-612 Apr 2004

[52] Lin Zhang Lei Zhang Xuanqin Mou and David Zhang FSIM a feature similarity index for image quality assessment IEEE Transactions on Image Processing vol 20 no 8 pp 2378-2386 2011

[53] P Kovesi ldquoImage features from phase congruencyrdquo Videre J Comp Vis Res vol 1 no 3 pp 1-26 1999

[54] L Henriksson A Hyvaumlrinen and S Vanni ldquoRepresentation of cross-frequency spatial phase relationships in human visual cortexrdquo J Neuroscience vol 29 no 45 pp 14342-14351 Nov 2009

[55] C Mancas-Thillou and B Gosselin ldquoCharacter segmentation-by-recognition using log-Gabor filtersrdquo in Proc Int Conf Pattern Recognit 2006 pp 901-904

[56] S Fischer F Šroubek L Perrinet R Redondo and G Cristoacutebal ldquoSelf-invertible 2D log-Gabor waveletsrdquo Int J Computer Vision vol 75 no 2 pp 231-246 Nov 2007

[57] W Wang J Li F Huang and H Feng ldquoDesign and implementation of log-Gabor filter in fingerprint image enhancementrdquo Pattern Recognit Letters vol 29 no 3 pp 301-308 Feb 2008

[58] H R Sheikh and A C Bovik Image information and visual quality IEEE Trans Image Processing vol 15 pp 430-444 Feb 2006

[59] Z Wang Rate scalable foveated image and video communications PhD thesis Dept of ECE the University of Texas at Austin Dec 2001

[60] Z Wang and A C Bovik A universal image quality index IEEE Signal Processing Letters vol 9 pp 81-84 March 2002

International Journal of Pure and Applied Mathematics Special Issue

144

145

146

145

146

146